diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.ats b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.ats
new file mode 100644
index 00000000000..b7f470b932f
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.ats
@@ -0,0 +1,18 @@
+from geos.ats.test_builder import TestDeck, RestartcheckParameters, generate_geos_tests
+
+restartcheck_params = {}
+restartcheck_params['atol'] = 1.0E-8
+restartcheck_params['rtol'] = 1.0E-8
+
+decks = [
+    TestDeck(
+        name="immiscibleTwoPhase_GravitySegregation_1d",
+        description=
+        'Test that 2 fluids can be seperated based on gravity.',
+        partitions=((1, 1, 1), ),
+        restart_step=0,
+        check_step=45,
+        restartcheck_params=RestartcheckParameters(**restartcheck_params))
+]
+
+generate_geos_tests(decks)
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.xml b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.xml
new file mode 100644
index 00000000000..62d4f6cf3bb
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.xml
@@ -0,0 +1,203 @@
+<?xml version="1.0"?>
+
+<Problem>
+  <Solvers
+    gravityVector="{ 0.0, 0.0, -10 }">
+    <ImmiscibleMultiphaseFlow
+      name="FlowSolver"
+      discretization="TPFA"
+      targetRegions="{ Domain }"
+      writeLinearSystem="0"
+      temperature="300"
+      initialDt="0.001">
+      <NonlinearSolverParameters
+        newtonTol="1.0e-6"
+        lineSearchAction="None"
+        newtonMaxIter="10" />
+      <LinearSolverParameters
+        directParallel="0" />
+    </ImmiscibleMultiphaseFlow>
+  </Solvers>
+
+  <Mesh>
+    <InternalMesh
+      name="mesh1"
+      elementTypes="{ C3D8 }"
+      xCoords="{ 0, 1 }"
+      yCoords="{ 0, 1 }"
+      zCoords="{ 0, 10 }"
+      nx="{ 1 }"
+      ny="{ 1 }"
+      nz="{ 10 }"
+      cellBlockNames="{ block1 }" />
+  </Mesh>
+  
+  <Geometry>
+    <Box
+      name="sink"
+      xMin="{ -0.01, -0.01, -0.01 }"
+      xMax="{ 1.01, 1.01, 1.01 }" />
+  </Geometry>
+
+  <Events
+    maxTime="0.4">
+    <PeriodicEvent
+      name="outputs"
+      timeFrequency="0.01"
+      target="/Outputs/vtkOutput" />
+
+    <PeriodicEvent
+      name="solverApplications"
+      target="/Solvers/FlowSolver" />
+
+    <PeriodicEvent
+      name="restarts"
+      timeFrequency="0.1"
+      targetExactTimestep="0"
+      target="/Outputs/restartOutput"/>
+  </Events>
+
+  <NumericalMethods>
+    <FiniteVolume>
+      <TwoPointFluxApproximation
+        name="TPFA" />
+    </FiniteVolume>
+  </NumericalMethods>
+
+  <ElementRegions>
+    <CellElementRegion
+      name="Domain"
+      cellBlocks="{ block1 }"
+      materialList="{ fluid, rock, relperm }" />
+  </ElementRegions>
+
+  <Functions>
+    <TableFunction
+      name="densityTablePhase1"
+      coordinates="{ 0.0}"
+      values="{ 10 }" />
+
+    <TableFunction
+      name="densityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 1 }" />
+
+    <TableFunction
+      name="viscosityTablePhase1"
+      coordinates="{ 0.0 }"
+      values="{ 1.0 }" />
+
+    <TableFunction
+      name="viscosityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 1.0 }" />
+
+    <TableFunction
+      name="saturationTable1"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialSaturation1.txt"
+      interpolation="nearest" />
+
+    <TableFunction
+      name="saturationTable2"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialSaturation2.txt"
+      interpolation="nearest" />
+    
+    <TableFunction
+      name="pressureTable"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialPressure.txt"
+      interpolation="nearest" />
+  </Functions>
+
+  <Constitutive>
+    <TwoPhaseImmiscibleFluid
+      name="fluid"
+      phaseNames="{ water, gas }"
+      densityTableNames="{ densityTablePhase1, densityTablePhase2 }"
+      viscosityTableNames="{ viscosityTablePhase1, viscosityTablePhase2 }" />
+
+    <CompressibleSolidConstantPermeability
+      name="rock"
+      solidModelName="nullSolid"
+      porosityModelName="rockPorosity"
+      permeabilityModelName="rockPerm" />
+
+    <NullModel
+      name="nullSolid" />
+
+    <PressurePorosity
+      name="rockPorosity"
+      defaultReferencePorosity="1.0"
+      referencePressure="0.0"
+      compressibility="1e-9" />
+
+    <ConstantPermeability
+      name="rockPerm"
+      permeabilityComponents="{ 1, 1, 1 }" />
+
+    <BrooksCoreyRelativePermeability
+      name="relperm"
+      phaseNames="{ water, oil }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseRelPermExponent="{ 1.0, 1.0 }"
+      phaseRelPermMaxValue="{ 1.0, 1.0 }" />
+  </Constitutive>
+
+  <FieldSpecifications>
+    <FieldSpecification
+      name="Porosity"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/Domain/block1"
+      fieldName="rockPorosity_referencePorosity"
+      scale="1.0" />
+
+    <FieldSpecification
+      name="initialPressure"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/Domain/block1"
+      fieldName="pressure"
+      scale="1.0"
+      functionName="pressureTable" />
+
+    <FieldSpecification
+      name="initialSat1"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/Domain/block1"
+      fieldName="phaseVolumeFraction"
+      component="0"
+      scale="1.0"
+      functionName="saturationTable1" />
+
+    <FieldSpecification
+      name="initialSat2"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/Domain/block1"
+      fieldName="phaseVolumeFraction"
+      component="1"
+      scale="1.0"
+      functionName="saturationTable2" />
+
+    <FieldSpecification
+      name="sinkTermP"
+      objectPath="ElementRegions/Domain/block1"
+      fieldName="pressure"
+      scale="500.0"
+      setNames="{ sink }" />
+  </FieldSpecifications>
+
+  <Outputs>
+    <VTK
+      name="vtkOutput" />
+    <Restart
+      name="restartOutput"/>      
+  </Outputs>
+</Problem>
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialPressure.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialPressure.txt
new file mode 100644
index 00000000000..85a30e13876
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialPressure.txt
@@ -0,0 +1,10 @@
+495.0
+485.0
+475.0
+465.0
+455.0
+400.0
+300.0
+200.0
+100.0
+0.0
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation1.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation1.txt
new file mode 100644
index 00000000000..99f11f6b2e7
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation1.txt
@@ -0,0 +1,10 @@
+0
+0
+0
+0
+0
+1
+1
+1
+1
+1
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation2.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation2.txt
new file mode 100644
index 00000000000..1c03b9c1871
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation2.txt
@@ -0,0 +1,10 @@
+1
+1
+1
+1
+1
+0
+0
+0
+0
+0
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/x.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/x.txt
new file mode 100644
index 00000000000..2eb3c4fe4ee
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/x.txt
@@ -0,0 +1 @@
+0.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/y.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/y.txt
new file mode 100644
index 00000000000..2eb3c4fe4ee
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/y.txt
@@ -0,0 +1 @@
+0.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/z.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/z.txt
new file mode 100644
index 00000000000..f43a1f14d26
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/z.txt
@@ -0,0 +1,10 @@
+0.5
+1.5
+2.5
+3.5
+4.5
+5.5
+6.5
+7.5
+8.5
+9.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialPressure.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialPressure.txt
new file mode 100644
index 00000000000..63943bfa00d
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialPressure.txt
@@ -0,0 +1,10 @@
+1e7
+1e7
+1e7
+1e7
+1e7
+1e7
+1e7
+1e7
+1e7
+1e7
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation1.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation1.txt
new file mode 100644
index 00000000000..1859fabae78
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation1.txt
@@ -0,0 +1,10 @@
+0.95
+0.95
+0.95
+0.95
+0.95
+0.95
+0.95
+0.05
+0.05
+0.05
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation2.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation2.txt
new file mode 100644
index 00000000000..d113536f2fd
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation2.txt
@@ -0,0 +1,10 @@
+0.05
+0.05
+0.05
+0.05
+0.05
+0.05
+0.05
+0.95
+0.95
+0.95
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/jFunction_linear.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/jFunction_linear.txt
new file mode 100644
index 00000000000..c3dfd50073f
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/jFunction_linear.txt
@@ -0,0 +1,2 @@
+4.33172935918785
+1.66604975353379
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permx.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permx.geos
new file mode 100644
index 00000000000..4d47d8fa568
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permx.geos
@@ -0,0 +1,10 @@
+50
+50
+50
+50
+50
+200
+200
+200
+200
+200
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permy.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permy.geos
new file mode 100644
index 00000000000..4d47d8fa568
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permy.geos
@@ -0,0 +1,10 @@
+50
+50
+50
+50
+50
+200
+200
+200
+200
+200
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permz.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permz.geos
new file mode 100644
index 00000000000..4d47d8fa568
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permz.geos
@@ -0,0 +1,10 @@
+50
+50
+50
+50
+50
+200
+200
+200
+200
+200
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/phaseVolumeFraction_water_linear.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/phaseVolumeFraction_water_linear.txt
new file mode 100644
index 00000000000..0d66ea1aee9
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/phaseVolumeFraction_water_linear.txt
@@ -0,0 +1,2 @@
+0
+1
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction
new file mode 100644
index 00000000000..e69de29bb2d
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction.txt
new file mode 100644
index 00000000000..72a78a75b85
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction.txt
@@ -0,0 +1,76 @@
+99.9980934
+17.78445609
+11.20350909
+8.549878542
+7.057769576
+6.082201546
+5.386086427
+4.86006559
+4.446116454
+4.110353325
+3.831547061
+3.595663494
+3.393021946
+3.216710174
+3.061649542
+2.924017691
+2.800877928
+2.68993357
+2.589360389
+2.497689435
+2.413723433
+2.336475912
+2.265126101
+2.198985069
+2.137469915
+2.080083807
+2.02640045
+1.976051821
+1.928718377
+1.884121218
+1.842015737
+1.802186411
+1.764442543
+1.728614745
+1.694551981
+1.662119113
+1.631194842
+1.601669938
+1.573445757
+1.546432977
+1.520550493
+1.495724483
+1.471887601
+1.448978263
+1.426940034
+1.405721104
+1.385273798
+1.365554178
+1.346521677
+1.328138769
+1.310370692
+1.293185194
+1.276552299
+1.260444114
+1.244834648
+1.229699646
+1.215016445
+1.200763848
+1.186921998
+1.173472275
+1.160397205
+1.147680364
+1.135306301
+1.123260469
+1.111529155
+1.100099423
+1.088959056
+1.078096509
+1.067500858
+1.057161765
+1.047069433
+1.03721457
+1.027588362
+1.018182437
+1.008988837
+0.999999998
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction_linear.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction_linear.txt
new file mode 100644
index 00000000000..13036f8fd03
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction_linear.txt
@@ -0,0 +1,2 @@
+100.00
+1.00
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water.txt
new file mode 100644
index 00000000000..f38627d4e85
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water.txt
@@ -0,0 +1,76 @@
+0.001
+0.013333333
+0.026666667
+0.04
+0.053333333
+0.066666667
+0.08
+0.093333333
+0.106666667
+0.12
+0.133333333
+0.146666667
+0.16
+0.173333333
+0.186666667
+0.2
+0.213333333
+0.226666667
+0.24
+0.253333333
+0.266666667
+0.28
+0.293333333
+0.306666667
+0.32
+0.333333333
+0.346666667
+0.36
+0.373333333
+0.386666667
+0.4
+0.413333333
+0.426666667
+0.44
+0.453333333
+0.466666667
+0.48
+0.493333333
+0.506666667
+0.52
+0.533333333
+0.546666667
+0.56
+0.573333333
+0.586666667
+0.6
+0.613333333
+0.626666667
+0.64
+0.653333333
+0.666666667
+0.68
+0.693333333
+0.706666667
+0.72
+0.733333333
+0.746666667
+0.76
+0.773333333
+0.786666667
+0.8
+0.813333333
+0.826666667
+0.84
+0.853333333
+0.866666667
+0.88
+0.893333333
+0.906666667
+0.92
+0.933333333
+0.946666667
+0.96
+0.973333333
+0.986666667
+1
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water_linear.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water_linear.txt
new file mode 100644
index 00000000000..0a269ee3741
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water_linear.txt
@@ -0,0 +1,2 @@
+0.0
+1.0
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_base.xml b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_base.xml
new file mode 100644
index 00000000000..efbd5b34421
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_base.xml
@@ -0,0 +1,293 @@
+<?xml version="1.0" ?>
+
+<Problem>
+  <!-- SPHINX_SOLVER -->
+  <Solvers
+   gravityVector="{ 0.0, 0.0, 9.81 }">
+    <ImmiscibleMultiphaseFlow
+      name="FlowSolver"
+      logLevel="2"
+      discretization="TPFA"
+      temperature="300"
+      initialDt="0.001"
+      targetRegions="{ region_left, region_right }"
+      interfaceFaceSetNames = "{ Interface }">
+      <NonlinearSolverParameters
+        newtonTol="1.0e-5"
+        newtonMaxIter="20"
+        maxTimeStepCuts="20"
+	maxSubSteps="2000"/>
+      <LinearSolverParameters
+        solverType="direct"
+        directParallel="0"  
+        logLevel="0"/>
+    </ImmiscibleMultiphaseFlow>  
+  </Solvers>
+  <!-- SPHINX_SOLVER_END -->
+ 
+  <!-- SPHINX_NUMERICAL -->
+  <NumericalMethods>
+    <FiniteVolume>
+      <TwoPointFluxApproximation
+        name="TPFA"/>
+    </FiniteVolume>
+  </NumericalMethods>
+  <!-- SPHINX_NUMERICAL_END -->
+
+  <!-- SPHINX_ELEMENTREGIONS -->
+  <ElementRegions>
+    <CellElementRegion
+      name="region_left"
+      cellBlocks="{ cb_left }"
+      materialList="{ fluid_left, rock, relperm_left, capPressure_left }"/>
+
+    <CellElementRegion
+      name="region_right"
+      cellBlocks="{ cb_right }"
+      materialList="{ fluid_right, rock, relperm_right, capPressure_right }"/>      
+
+    <SurfaceElementRegion
+      name="Interface"
+      defaultAperture="1.0e-5"
+      materialList="{ fluid_left, fluid_right }"/>
+
+  </ElementRegions>
+  <!-- SPHINX_ELEMENTREGIONS_END -->
+
+  <!-- SPHINX_MATERIAL -->
+  <Functions>
+    <TableFunction
+      name="densityTablePhase1"
+      coordinates="{ 0.0}"
+      values="{ 900 }" />
+    <TableFunction
+      name="densityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 400 }" />
+    <TableFunction
+      name="viscosityTablePhase1"
+      coordinates="{ 0.0}"
+      values="{ 0.001 }" />                  
+    <TableFunction
+      name="viscosityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 0.001 }" />
+    <TableFunction
+      name="saturationTable1"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialSaturation1.txt"
+      interpolation="nearest" />
+    <TableFunction
+      name="saturationTable2"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialSaturation2.txt"
+      interpolation="nearest" />
+    <TableFunction
+      name="pressureTable"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialPressure.txt"
+      interpolation="nearest" />
+   <TableFunction
+      name="jFunctionTable"
+      coordinateFiles="{ tables/phaseVolumeFraction_water.txt }"
+      voxelFile="tables/jFunction.txt"/>
+    <TableFunction 
+      name="permxFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{x.txt,y.txt,z.txt}"
+      voxelFile="permx.geos"
+      interpolation="nearest" />
+    <TableFunction 
+      name="permyFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{x.txt,y.txt,z.txt}"
+      voxelFile="permy.geos"
+      interpolation="nearest" />
+    <TableFunction 
+      name="permzFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{x.txt,y.txt,z.txt}"
+      voxelFile="permz.geos"
+      interpolation="nearest" />
+      
+ </Functions>
+
+  <Constitutive>
+    <CompressibleSolidConstantPermeability
+      name="rock"
+      solidModelName="nullSolid"
+      porosityModelName="rockPorosity"
+      permeabilityModelName="rockPerm"/>
+
+    <NullModel
+      name="nullSolid"/>
+
+    <PressurePorosity
+      name="rockPorosity"
+      defaultReferencePorosity="0.25"
+      referencePressure="1e7"
+      compressibility="1.0e-15"/>
+
+    <ConstantPermeability
+      name="rockPerm"
+      permeabilityComponents="{ 1.0e-14, 1.0e-14, 1.0e-14}"/>   
+
+    <BrooksCoreyRelativePermeability
+      name="relperm_left"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseRelPermExponent="{ 1.5, 1.5 }"
+      phaseRelPermMaxValue="{ 1.0, 1.0 }"/>
+
+    <BrooksCoreyRelativePermeability
+      name="relperm_right"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseRelPermExponent="{ 1.5, 1.5 }"
+      phaseRelPermMaxValue="{ 1.0, 1.0 }"/>
+
+  <!--  <JFunctionCapillaryPressure
+      name="capPressure_left"
+      phaseNames="{ water, gas }" 
+      wettingNonWettingJFunctionTableName="jFunctionTable"
+      wettingNonWettingSurfaceTension="6.12e-3"
+      permeabilityDirection="XY"/>
+
+    <JFunctionCapillaryPressure
+      name="capPressure_right"
+      phaseNames="{ water, gas }" 
+      wettingNonWettingJFunctionTableName="jFunctionTable"
+      wettingNonWettingSurfaceTension="6.12e-3"
+      permeabilityDirection="XY"/> -->   
+
+<BrooksCoreyCapillaryPressure
+      name="capPressure_left"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseCapPressureExponentInv="{ 4 , 1 }"
+      phaseEntryPressure="{ 4e3, 0 }"
+      capPressureEpsilon="1e-8" />
+
+<BrooksCoreyCapillaryPressure
+      name="capPressure_right"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseCapPressureExponentInv="{ 4 , 1 }"
+      phaseEntryPressure="{ 2e3, 0 }"
+      capPressureEpsilon="1e-8" />
+
+    <TwoPhaseImmiscibleFluid
+      name="fluid_left"
+      phaseNames="{ water, gas }"
+      densityTableNames="{densityTablePhase1, densityTablePhase2}"    
+      viscosityTableNames="{viscosityTablePhase1, viscosityTablePhase2}" />
+
+    <TwoPhaseImmiscibleFluid
+      name="fluid_right"
+      phaseNames="{ water, gas }"
+      densityTableNames="{densityTablePhase1, densityTablePhase2}"    
+      viscosityTableNames="{viscosityTablePhase1, viscosityTablePhase2}" />
+
+  </Constitutive>
+  <!-- SPHINX_MATERIAL_END -->
+
+  <!-- SPHINX_BC --> 
+  <FieldSpecifications>
+    <FieldSpecification
+      name="Porosity"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPorosity_referencePorosity"
+      scale="0.25" />
+
+    <FieldSpecification
+      name="initialPressure"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="pressure"
+      scale="1.0"
+      functionName="pressureTable" />
+
+    <FieldSpecification
+      name="initialSaturation1"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="phaseVolumeFraction"
+      component="0"
+      scale="1.0"
+      functionName="saturationTable1" />
+
+    <FieldSpecification
+      name="initialSaturation2"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="phaseVolumeFraction"
+      component="1"
+      scale="1.0"
+      functionName="saturationTable2" />
+
+   <FieldSpecification
+      name="permx"
+      component="0"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permxFunc"
+      scale="1.0e-14"/>
+
+    <FieldSpecification
+      name="permy"
+      component="1"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permyFunc"
+      scale="1.0e-14"/>
+
+    <FieldSpecification
+      name="permz"
+      component="2"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permzFunc"
+      scale="1.0e-14"/>
+
+  </FieldSpecifications>
+  <!-- SPHINX_BC_END -->
+
+  <!-- SPHINX_OUTPUT -->  
+  <Outputs>
+    <VTK
+      name="vtkOutput"/>
+<!--
+    <TimeHistory
+      name="timeHistoryOutput"
+      sources="{/Tasks/phaseVolumeFractionCollection}"
+      filename="saturationHistory" />
+-->
+    <Restart
+      name="restartOutput"/> 
+  </Outputs>
+  <!-- SPHINX_OUTPUT_END -->
+
+  <!-- SPHINX_TASKS --> 
+<!--  <Tasks>
+    <PackCollection
+      name="phaseVolumeFractionCollection"
+      objectPath="ElementRegions/region_left/cb_left"
+      fieldName="phaseVolumeFraction"/>      
+  </Tasks>
+-->
+  <!-- SPHINX_TASKS_END -->   
+</Problem>
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_interface_condition.xml b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_interface_condition.xml
new file mode 100644
index 00000000000..41ba4e3ed92
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_interface_condition.xml
@@ -0,0 +1,66 @@
+<?xml version="1.0" ?>
+
+<Problem>
+  <Included>
+    <File name="./uni_directional_flow_base.xml"/>
+  </Included>
+
+  <!-- SPHINX_MESH -->
+  <Mesh>
+    <InternalMesh
+      name="mesh"
+      elementTypes="{ C3D8 }"
+      xCoords="{ 0, 1 }"
+      yCoords="{ 0, 1 }"
+      zCoords="{ 0, 5, 10 }"
+      nx="{ 1 }"
+      ny="{ 1 }"
+      nz="{ 10, 10 }"
+      cellBlockNames="{ cb_left, cb_right }"/>
+  </Mesh>
+  <!-- SPHINX_MESH_END -->
+
+  <Geometry>
+<!--    <Box
+      name="source"
+      xMin="{0.0, -0.00001, -0.00001}"
+      xMax="{0.01, 1.00001, 1.00001}"/> -->
+
+    <Box
+      name="sink"
+      xMin="{ -0.00001, -0.00001, -0.00001}"
+      xMax="{ 1.00001, 1.00001, 1.00001}"/>
+
+    <Box
+      name="Interface"
+      xMin="{ -0.01, -0.01, 4.99 }"
+      xMax="{  1.01, 1.01, 5.01 }"/>      
+  </Geometry>
+
+  <Events
+    maxTime="86.4e+05">
+      
+    <PeriodicEvent
+      name="outputs"
+      timeFrequency="86.4e+03"
+      targetExactTimestep="1"
+      target="/Outputs/vtkOutput"/>
+<!--
+    <PeriodicEvent
+      name="timeHistoryOutput"
+      timeFrequency="20000"
+      targetExactTimestep="1"
+      target="/Outputs/timeHistoryOutput" />
+
+    <PeriodicEvent
+      name="timeHistoryCollection"
+      timeFrequency="20000"
+      targetExactTimestep="1"
+      target="/Tasks/phaseVolumeFractionCollection" />
+-->
+    <PeriodicEvent
+      name="solverApplications"
+      maxEventDt="86.4e+03"
+      target="/Solvers/FlowSolver"/>    
+  </Events>
+</Problem>
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/x.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/x.txt
new file mode 100644
index 00000000000..2eb3c4fe4ee
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/x.txt
@@ -0,0 +1 @@
+0.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/y.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/y.txt
new file mode 100644
index 00000000000..2eb3c4fe4ee
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/y.txt
@@ -0,0 +1 @@
+0.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/z.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/z.txt
new file mode 100644
index 00000000000..f43a1f14d26
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/z.txt
@@ -0,0 +1,10 @@
+0.5
+1.5
+2.5
+3.5
+4.5
+5.5
+6.5
+7.5
+8.5
+9.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialPressure.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialPressure.txt
new file mode 100644
index 00000000000..6963bb6148c
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialPressure.txt
@@ -0,0 +1,1200 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation1.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation1.txt
new file mode 100644
index 00000000000..90ddc12151e
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation1.txt
@@ -0,0 +1,1200 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation2.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation2.txt
new file mode 100644
index 00000000000..d5ef52f254b
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation2.txt
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permx.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permx.geos
new file mode 100644
index 00000000000..439bd535a86
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permx.geos
@@ -0,0 +1,1200 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permy.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permy.geos
new file mode 100644
index 00000000000..439bd535a86
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permy.geos
@@ -0,0 +1,1200 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permz.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permz.geos
new file mode 100644
index 00000000000..439bd535a86
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permz.geos
@@ -0,0 +1,1200 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/x.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/x.txt
new file mode 100644
index 00000000000..283fc50e7fb
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/x.txt
@@ -0,0 +1,10 @@
+5.00000000e-01
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/y.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/y.txt
new file mode 100644
index 00000000000..a01763bc5d1
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/y.txt
@@ -0,0 +1,6 @@
+5.00000000e-01
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/z.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/z.txt
new file mode 100644
index 00000000000..d122a370abe
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/z.txt
@@ -0,0 +1,20 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_base.xml b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_base.xml
new file mode 100644
index 00000000000..3982a2b12c6
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_base.xml
@@ -0,0 +1,299 @@
+<?xml version="1.0" ?>
+
+<Problem>
+  <!-- SPHINX_SOLVER -->
+  <Solvers
+   gravityVector="{ 0.0, 0.0, 9.81 }">
+    <ImmiscibleMultiphaseFlow
+      name="FlowSolver"
+      logLevel="1"
+      discretization="TPFA"
+      temperature="300"
+      initialDt="0.001"
+      targetRegions="{ region_left, region_right }">
+      <!-- interfaceFaceSetNames = "{ Interface }"> -->
+      <NonlinearSolverParameters
+        newtonTol="1e-4"
+        newtonMaxIter="20"
+        maxTimeStepCuts="50"
+        maxSubSteps="100"
+        lineSearchAction="None"
+        timeStepDecreaseFactor="0.9"
+        timeStepIncreaseFactor="1.5" 
+        timeStepDecreaseIterLimit="0.8"
+        timeStepIncreaseIterLimit="0.6"/>
+<!--       <LinearSolverParameters
+        solverType="direct"
+        directParallel="0"  
+        logLevel="0"/> -->
+      <LinearSolverParameters solverType="gmres" preconditionerType="amg" krylovTol="1.0e-7" logLevel="1"/>        
+    </ImmiscibleMultiphaseFlow>  
+  </Solvers>
+  <!-- SPHINX_SOLVER_END -->
+ 
+  <!-- SPHINX_NUMERICAL -->
+  <NumericalMethods>
+    <FiniteVolume>
+      <TwoPointFluxApproximation
+        name="TPFA"/>
+    </FiniteVolume>
+  </NumericalMethods>
+  <!-- SPHINX_NUMERICAL_END -->
+
+  <!-- SPHINX_ELEMENTREGIONS -->
+  <ElementRegions>
+    <CellElementRegion
+      name="region_left"
+      cellBlocks="{ cb_left }"
+      materialList="{ fluid_left, rock, relperm_left, capPressure_left }"/>
+
+    <CellElementRegion
+      name="region_right"
+      cellBlocks="{ cb_right }"
+      materialList="{ fluid_right, rock, relperm_right, capPressure_right }"/>      
+
+    <SurfaceElementRegion
+      name="Interface"
+      defaultAperture="1.0e-5"
+      materialList="{ fluid_left, fluid_right }"/>
+
+  </ElementRegions>
+  <!-- SPHINX_ELEMENTREGIONS_END -->
+
+  <!-- SPHINX_MATERIAL -->
+  <Functions>
+    <TableFunction
+      name="densityTablePhase1"
+      coordinates="{ 0.0}"
+      values="{ 900 }" />
+    <TableFunction
+      name="densityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 400 }" />
+    <TableFunction
+      name="viscosityTablePhase1"
+      coordinates="{ 0.0}"
+      values="{ 0.001 }" />                  
+    <TableFunction
+      name="viscosityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 0.001 }" />
+    <TableFunction
+      name="saturationTable1"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ input/x.txt, input/y.txt, input/z.txt }"
+      voxelFile="input/initialSaturation1.txt"
+      interpolation="nearest" />
+    <TableFunction
+      name="saturationTable2"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ input/x.txt, input/y.txt, input/z.txt }"
+      voxelFile="input/initialSaturation2.txt"
+      interpolation="nearest" />
+    <TableFunction
+      name="pressureTable"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ input/x.txt, input/y.txt, input/z.txt }"
+      voxelFile="input/initialPressure.txt"
+      interpolation="nearest" />
+<!--   <TableFunction
+      name="jFunctionTable"
+      coordinateFiles="{ tables/phaseVolumeFraction_water.txt }"
+      voxelFile="tables/jFunction.txt"/> -->
+    <TableFunction 
+      name="permxFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{input/x.txt,input/y.txt,input/z.txt}"
+      voxelFile="input/permx.geos"
+      interpolation="nearest" />
+    <TableFunction 
+      name="permyFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{input/x.txt,input/y.txt,input/z.txt}"
+      voxelFile="input/permy.geos"
+      interpolation="nearest" />
+    <TableFunction 
+      name="permzFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{input/x.txt,input/y.txt,input/z.txt}"
+      voxelFile="input/permz.geos"
+      interpolation="nearest" />
+      
+ </Functions>
+
+  <Constitutive>
+    <CompressibleSolidConstantPermeability
+      name="rock"
+      solidModelName="nullSolid"
+      porosityModelName="rockPorosity"
+      permeabilityModelName="rockPerm"/>
+
+    <NullModel
+      name="nullSolid"/>
+
+    <PressurePorosity
+      name="rockPorosity"
+      defaultReferencePorosity="0.25"
+      referencePressure="1e7"
+      compressibility="1.0e-15"/>
+
+    <ConstantPermeability
+      name="rockPerm"
+      permeabilityComponents="{ 1.0e-14, 1.0e-14, 1.0e-14}"/>   
+
+    <BrooksCoreyRelativePermeability
+      name="relperm_left"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseRelPermExponent="{ 1.5, 1.5 }"
+      phaseRelPermMaxValue="{ 1.0, 1.0 }"/>
+
+    <BrooksCoreyRelativePermeability
+      name="relperm_right"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseRelPermExponent="{ 1.5, 1.5 }"
+      phaseRelPermMaxValue="{ 1.0, 1.0 }"/>
+
+  <!--  <JFunctionCapillaryPressure
+      name="capPressure_left"
+      phaseNames="{ water, gas }" 
+      wettingNonWettingJFunctionTableName="jFunctionTable"
+      wettingNonWettingSurfaceTension="6.12e-3"
+      permeabilityDirection="XY"/>
+
+    <JFunctionCapillaryPressure
+      name="capPressure_right"
+      phaseNames="{ water, gas }" 
+      wettingNonWettingJFunctionTableName="jFunctionTable"
+      wettingNonWettingSurfaceTension="6.12e-3"
+      permeabilityDirection="XY"/> -->   
+
+<BrooksCoreyCapillaryPressure
+      name="capPressure_left"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseCapPressureExponentInv="{ 4 , 1 }"
+      phaseEntryPressure="{ 4e3, 0 }"
+      capPressureEpsilon="1e-8" />
+
+<BrooksCoreyCapillaryPressure
+      name="capPressure_right"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseCapPressureExponentInv="{ 4 , 1 }"
+      phaseEntryPressure="{ 2e3, 0 }"
+      capPressureEpsilon="1e-8" />
+
+    <TwoPhaseImmiscibleFluid
+      name="fluid_left"
+      phaseNames="{ water, gas }"
+      densityTableNames="{densityTablePhase1, densityTablePhase2}"    
+      viscosityTableNames="{viscosityTablePhase1, viscosityTablePhase2}" />
+
+    <TwoPhaseImmiscibleFluid
+      name="fluid_right"
+      phaseNames="{ water, gas }"
+      densityTableNames="{densityTablePhase1, densityTablePhase2}"    
+      viscosityTableNames="{viscosityTablePhase1, viscosityTablePhase2}" />
+
+  </Constitutive>
+  <!-- SPHINX_MATERIAL_END -->
+
+  <!-- SPHINX_BC --> 
+  <FieldSpecifications>
+    <FieldSpecification
+      name="Porosity"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPorosity_referencePorosity"
+      scale="0.25" />
+
+    <FieldSpecification
+      name="initialPressure"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="pressure"
+      scale="1.0"
+      functionName="pressureTable" />
+
+    <FieldSpecification
+      name="initialSaturation1"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="phaseVolumeFraction"
+      component="0"
+      scale="1.0"
+      functionName="saturationTable1" />
+
+    <FieldSpecification
+      name="initialSaturation2"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="phaseVolumeFraction"
+      component="1"
+      scale="1.0"
+      functionName="saturationTable2" />
+
+   <FieldSpecification
+      name="permx"
+      component="0"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permxFunc"
+      scale="1.0e-14"/>
+
+    <FieldSpecification
+      name="permy"
+      component="1"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permyFunc"
+      scale="1.0e-14"/>
+
+    <FieldSpecification
+      name="permz"
+      component="2"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permzFunc"
+      scale="1.0e-14"/>
+
+  </FieldSpecifications>
+  <!-- SPHINX_BC_END -->
+
+  <!-- SPHINX_OUTPUT -->  
+  <Outputs>
+    <VTK
+      name="vtkOutput"/>
+<!--
+    <TimeHistory
+      name="timeHistoryOutput"
+      sources="{/Tasks/phaseVolumeFractionCollection}"
+      filename="saturationHistory" />
+-->
+    <Restart
+      name="restartOutput"/> 
+  </Outputs>
+  <!-- SPHINX_OUTPUT_END -->
+
+  <!-- SPHINX_TASKS --> 
+<!--  <Tasks>
+    <PackCollection
+      name="phaseVolumeFractionCollection"
+      objectPath="ElementRegions/region_left/cb_left"
+      fieldName="phaseVolumeFraction"/>      
+  </Tasks>
+-->
+  <!-- SPHINX_TASKS_END -->   
+</Problem>
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_interface_condition.xml b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_interface_condition.xml
new file mode 100644
index 00000000000..9bac844ae7b
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_interface_condition.xml
@@ -0,0 +1,66 @@
+<?xml version="1.0" ?>
+
+<Problem>
+  <Included>
+    <File name="./uni_directional_flow_base.xml"/>
+  </Included>
+
+  <!-- SPHINX_MESH -->
+  <Mesh>
+    <InternalMesh
+      name="mesh"
+      elementTypes="{ C3D8 }"
+      xCoords="{ 0, 10 }"
+      yCoords="{ 0, 6 }"
+      zCoords="{ 0, 5, 10 }"
+      nx="{ 40 }"
+      ny="{ 1 }"
+      nz="{ 40, 40 }"
+      cellBlockNames="{ cb_left, cb_right }"/>
+  </Mesh>
+  <!-- SPHINX_MESH_END -->
+
+  <Geometry>
+<!--    <Box
+      name="source"
+      xMin="{0.0, -0.00001, -0.00001}"
+      xMax="{0.01, 1.00001, 1.00001}"/> -->
+
+    <Box
+      name="sink"
+      xMin="{ -0.00001, -0.00001, -0.00001}"
+      xMax="{ 1.00001, 1.00001, 1.00001}"/>
+
+    <Box
+      name="Interface"
+      xMin="{ -0.01, -0.01, 4.99 }"
+      xMax="{  10.01, 6.01, 5.01 }"/>      
+  </Geometry>
+
+  <Events
+    maxTime="86.4e+05">
+      
+    <PeriodicEvent
+      name="outputs"
+      timeFrequency="86.4e+03"
+      targetExactTimestep="1"
+      target="/Outputs/vtkOutput"/>
+<!--
+    <PeriodicEvent
+      name="timeHistoryOutput"
+      timeFrequency="20000"
+      targetExactTimestep="1"
+      target="/Outputs/timeHistoryOutput" />
+
+    <PeriodicEvent
+      name="timeHistoryCollection"
+      timeFrequency="20000"
+      targetExactTimestep="1"
+      target="/Tasks/phaseVolumeFractionCollection" />
+-->
+    <PeriodicEvent
+      name="solverApplications"
+      maxEventDt="86.4e03"
+      target="/Solvers/FlowSolver"/>    
+  </Events>
+</Problem>
diff --git a/src/coreComponents/common/DataLayouts.hpp b/src/coreComponents/common/DataLayouts.hpp
index cd09af18ef0..0f23039b745 100644
--- a/src/coreComponents/common/DataLayouts.hpp
+++ b/src/coreComponents/common/DataLayouts.hpp
@@ -21,6 +21,7 @@
 #define GEOS_COMMON_DATALAYOUTS_HPP_
 
 #include "common/GeosxConfig.hpp"
+#include "common/DataTypes.hpp"
 
 #include "LvArray/src/Array.hpp"
 #include "RAJA/RAJA.hpp"
diff --git a/src/coreComponents/constitutive/CMakeLists.txt b/src/coreComponents/constitutive/CMakeLists.txt
index 6af439fe23f..f4d46708e56 100644
--- a/src/coreComponents/constitutive/CMakeLists.txt
+++ b/src/coreComponents/constitutive/CMakeLists.txt
@@ -369,6 +369,7 @@ if( ENABLE_PVTPackage )
 endif()
 
 if (ENABLE_HPCREACT)
+  if( EXISTS "${CMAKE_CURRENT_SOURCE_DIR}/HPCReact/CMakeLists.txt" )
     set( constitutive_headers
         ${constitutive_headers}
         fluid/reactivefluid/ReactiveFluidSelector.hpp 
@@ -383,8 +384,9 @@ if (ENABLE_HPCREACT)
          ${constitutive_sources}
          fluid/reactivefluid/ReactiveSinglePhaseFluid.cpp 
         )
-  add_subdirectory( HPCReact )
-  list( APPEND dependencyList hpcReact )
+    add_subdirectory( HPCReact )
+    list( APPEND dependencyList hpcReact )
+  endif()
 endif()
 
 geos_decorate_link_dependencies( LIST decoratedDependencies
diff --git a/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.hpp b/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.hpp
index 39d93e48858..39b61e786f7 100644
--- a/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.hpp
@@ -57,6 +57,11 @@ class BrooksCoreyCapillaryPressureUpdate final : public CapillaryPressureBaseUpd
                 arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
                 arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
 
+  GEOS_HOST_DEVICE
+  void computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+                   arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+                   arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
+
   GEOS_HOST_DEVICE
   virtual void update( localIndex const k,
                        localIndex const q,
@@ -80,14 +85,32 @@ class BrooksCoreyCapillaryPressureUpdate final : public CapillaryPressureBaseUpd
                                real64 & phaseCapPressure,
                                real64 & dPhaseCapPressure_dVolFrac );
 
+
+  GEOS_HOST_DEVICE
+  GEOS_FORCE_INLINE
+  static void
+  evaluateBrooksCoreyFunctionInv( real64 const phaseCapPressure,
+                                  int const ip,
+                                  real64 const volFracScaleInv,
+                                  real64 const exponentInv,
+                                  real64 const entryPressure,
+                                  real64 const maxCapPres_eps,
+                                  real64 const phaseMinVolumeFraction,
+                                  arrayView1d< integer const > const phaseOrder,
+                                  real64 & phaseVolFraction,
+                                  real64 & dPhaseCapPressure_dVolFrac );
+
   arrayView1d< real64 const > m_phaseMinVolumeFraction;
   arrayView1d< real64 const > m_phaseCapPressureExponentInv;
   arrayView1d< real64 const > m_phaseEntryPressure;
 
   real64 m_capPressureEpsilon;
   real64 m_volFracScale;
+
 };
 
+
+
 class BrooksCoreyCapillaryPressure : public CapillaryPressureBase
 {
 public:
@@ -169,11 +192,14 @@ BrooksCoreyCapillaryPressureUpdate::
 
   // compute first gas-oil capillary pressure as a function of gas-phase vol fraction
   integer const ip_gas = m_phaseOrder[CapillaryPressureBase::PhaseType::GAS];
-  if( ip_gas >= 0 )
+  integer const ip_oil = m_phaseOrder[CapillaryPressureBase::PhaseType::OIL];
+
+  GEOS_UNUSED_VAR( ip_gas );
+  if( ip_oil >= 0 )
   {
-    real64 const volFracScaled = (phaseVolFraction[ip_gas] - m_phaseMinVolumeFraction[ip_gas]) * volFracScaleInv;
-    real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_gas];
-    real64 const entryPressure = -m_phaseEntryPressure[ip_gas]; // for gas capillary pressure, take the opposite of the
+    real64 const volFracScaled = (phaseVolFraction[ip_oil] - m_phaseMinVolumeFraction[ip_oil]) * volFracScaleInv;
+    real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_oil];
+    real64 const entryPressure = -m_phaseEntryPressure[ip_oil]; // for gas capillary pressure, take the opposite of the
                                                                 // BC function
 
     real64 const wettingVolFracScaled           = 1-volFracScaled;
@@ -184,11 +210,103 @@ BrooksCoreyCapillaryPressureUpdate::
                                  exponentInv,
                                  entryPressure,
                                  eps,
-                                 phaseCapPres[ip_gas],
-                                 dPhaseCapPres_dPhaseVolFrac[ip_gas][ip_gas] );
+                                 phaseCapPres[ip_oil],
+                                 dPhaseCapPres_dPhaseVolFrac[ip_oil][ip_oil] );
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+BrooksCoreyCapillaryPressureUpdate::
+  computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+              arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+              arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const
+{
+  LvArray::forValuesInSlice( dPhaseCapPres_dPhaseVolFrac, []( real64 & val ){ val = 0.0; } );
+
+  real64 const volFracScaleInv = 1.0 / m_volFracScale;
+
+  // the Brooks-Corey model does not support volFracScaled = 0,
+  // hence we need an epsilon value to avoid a division by zero
+  // TODO: for S < epsilon, replace the original unbounded BC curve with a bounded power-law extension
+  real64 const eps = m_capPressureEpsilon;
+
+
+  // compute first water-oil capillary pressure as a function of water-phase vol fraction
+  integer const ip_water = m_phaseOrder[CapillaryPressureBase::PhaseType::WATER];
+  integer const ip_gas = m_phaseOrder[CapillaryPressureBase::PhaseType::GAS];
+  if( ip_water >= 0 )
+  {
+    real64 const volFracScaled_eps = (eps - m_phaseMinVolumeFraction[ip_water]) * volFracScaleInv;
+    real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_water];
+    real64 const entryPressure = m_phaseEntryPressure[ip_water];
+
+    real64 const wettingVolFracScaled_eps           = volFracScaled_eps;
+    real64 const dWettingVolFracScaled_dVolFrac = volFracScaleInv;
+
+    real64 maxCapPres_eps = 0.0;
+    real64 max_dpc_eps = 0.0;
+
+    evaluateBrooksCoreyFunction( wettingVolFracScaled_eps,
+                                 dWettingVolFracScaled_dVolFrac,
+                                 exponentInv,
+                                 entryPressure,
+                                 eps,
+                                 maxCapPres_eps,
+                                 max_dpc_eps );
+
+    evaluateBrooksCoreyFunctionInv( phaseCapPres[ip_water],
+                                    ip_water,
+                                    volFracScaleInv,
+                                    exponentInv,
+                                    entryPressure,
+                                    maxCapPres_eps,
+                                    m_phaseMinVolumeFraction[ip_water],
+                                    m_phaseOrder,
+                                    phaseVolFraction[ip_water],
+                                    dPhaseCapPres_dPhaseVolFrac[ip_water][ip_water] );
+    phaseVolFraction[ip_gas] = 1.0 - phaseVolFraction[ip_water];
+  }
+
+
+  // compute first gas-oil capillary pressure as a function of gas-phase vol fraction
+
+
+  // if( ip_gas >= 0 )
+  // {
+  //   real64 const volFracScaled_eps = (eps - m_phaseMinVolumeFraction[ip_gas]) * volFracScaleInv;
+  //   real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_gas];
+  //   real64 const entryPressure = -m_phaseEntryPressure[ip_gas]; // for gas capillary pressure, take the opposite of the
+  //                                                               // BC function
+
+  //   real64 const wettingVolFracScaled_eps           = 1-volFracScaled_eps;
+  //   real64 const dWettingVolFracScaled_dVolFrac =  -volFracScaleInv;
+
+  //   real64 maxCapPres_eps = 0.0;
+  //   real64 max_dpc_eps = 0.0;
+
+  //   evaluateBrooksCoreyFunction( wettingVolFracScaled_eps,
+  //                                dWettingVolFracScaled_dVolFrac,
+  //                                exponentInv,
+  //                                entryPressure,
+  //                                eps,
+  //                                maxCapPres_eps,
+  //                                max_dpc_eps );
+
+  //   evaluateBrooksCoreyFunctionInv( phaseCapPres[ip_gas],
+  //                                   ip_gas,
+  //                                   volFracScaleInv,
+  //                                   exponentInv,
+  //                                   entryPressure,
+  //                                   maxCapPres_eps,
+  //                                   m_phaseMinVolumeFraction[ip_gas],
+  //                                   m_phaseOrder,
+  //                                   phaseVolFraction[ip_gas],
+  //                                   dPhaseCapPres_dPhaseVolFrac[ip_gas][ip_gas] );
+  //  phaseVolFraction[ip_water] = 1.0 - phaseVolFraction[ip_gas];
+  // }
+}
+
 GEOS_HOST_DEVICE
 inline void
 BrooksCoreyCapillaryPressureUpdate::
@@ -222,6 +340,49 @@ BrooksCoreyCapillaryPressureUpdate::
 
 }
 
+GEOS_HOST_DEVICE
+inline void
+BrooksCoreyCapillaryPressureUpdate::
+  evaluateBrooksCoreyFunctionInv( real64 const phaseCapPressure,
+                                  int const ip,
+                                  real64 const volFracScaleInv,
+                                  real64 const exponentInv,
+                                  real64 const entryPressure,
+                                  real64 const maxCapPres_eps,
+                                  real64 const phaseMinVolumeFraction,
+                                  arrayView1d< integer const > const phaseOrder,
+                                  real64 & phaseVolFraction,
+                                  real64 & dPhaseCapPressure_dVolFrac )
+{
+
+
+  phaseVolFraction           = 0.0;
+  real64 value               = 0.0;
+  dPhaseCapPressure_dVolFrac = 0.0;
+  integer const ip_oil = phaseOrder[CapillaryPressureBase::PhaseType::OIL];
+
+  real64 const dScaledWettingPhaseVolFrac_dVolFrac = (ip == ip_oil)
+  ? -volFracScaleInv : volFracScaleInv;
+
+  if( phaseCapPressure <= maxCapPres_eps && phaseCapPressure >= entryPressure )
+  {
+    // intermediate value
+    real64 const val =  pow( entryPressure, exponentInv ) / pow( phaseCapPressure, exponentInv + 1 );
+
+    value           = (phaseCapPressure  * val) * volFracScaleInv + phaseMinVolumeFraction; // entryPressure * (S_w)^( - 1 / exponentInv )
+    dPhaseCapPressure_dVolFrac = -dScaledWettingPhaseVolFrac_dVolFrac * val * exponentInv;
+    phaseVolFraction = (ip == ip_oil) ? 1.0 - value : value;
+  }
+  else // enforce a constant and bounded capillary pressure
+  {
+    real64 const val = (phaseCapPressure > maxCapPres_eps)
+                     ? pow( entryPressure, exponentInv ) / pow( maxCapPres_eps, exponentInv ) : 1.0;
+    value           = val * volFracScaleInv + phaseMinVolumeFraction;
+    phaseVolFraction = (ip == ip_oil) ? 1.0 - value : value;
+  }
+
+}
+
 
 } // namespace constitutive
 
diff --git a/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureSelector.hpp b/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureSelector.hpp
index b164f55aa16..c9b96e018b7 100644
--- a/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureSelector.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureSelector.hpp
@@ -36,20 +36,24 @@ template< typename LAMBDA >
 void constitutiveUpdatePassThru( CapillaryPressureBase const & capPres,
                                  LAMBDA && lambda )
 {
-  ConstitutivePassThruHandler< BrooksCoreyCapillaryPressure,
-                               JFunctionCapillaryPressure,
-                               TableCapillaryPressure,
-                               VanGenuchtenCapillaryPressure >::execute( capPres, std::forward< LAMBDA >( lambda ) );
+  ConstitutivePassThruHandler<
+    BrooksCoreyCapillaryPressure,
+    JFunctionCapillaryPressure,
+    TableCapillaryPressure,
+    VanGenuchtenCapillaryPressure
+    >::execute( capPres, std::forward< LAMBDA >( lambda ) );
 }
 
 template< typename LAMBDA >
 void constitutiveUpdatePassThru( CapillaryPressureBase & capPres,
                                  LAMBDA && lambda )
 {
-  ConstitutivePassThruHandler< BrooksCoreyCapillaryPressure,
-                               JFunctionCapillaryPressure,
-                               TableCapillaryPressure,
-                               VanGenuchtenCapillaryPressure >::execute( capPres, std::forward< LAMBDA >( lambda ) );
+  ConstitutivePassThruHandler<
+    BrooksCoreyCapillaryPressure,
+    JFunctionCapillaryPressure,
+    TableCapillaryPressure,
+    VanGenuchtenCapillaryPressure
+    >::execute( capPres, std::forward< LAMBDA >( lambda ) );
 }
 
 } // namespace constitutive
diff --git a/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.cpp b/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.cpp
index e4eb76d02ba..320c940716c 100644
--- a/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.cpp
+++ b/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.cpp
@@ -119,6 +119,14 @@ JFunctionCapillaryPressure::JFunctionCapillaryPressure( std::string const & name
     .setInputFlag( InputFlags::FALSE );
 
   registerField< fields::cappres::jFuncMultiplier >( &m_jFuncMultiplier );
+
+  registerWrapper( viewKeyStruct::jFunctionWrappersString(), &m_jFuncKernelWrappers ).
+    setSizedFromParent( 0 ).
+    setRestartFlags( RestartFlags::NO_WRITE );
+
+  registerWrapper( viewKeyStruct::inverseJFunctionWrappersString(), &m_inverseJFuncKernelWrappers ).
+    setSizedFromParent( 0 ).
+    setRestartFlags( RestartFlags::NO_WRITE );
 }
 
 void JFunctionCapillaryPressure::postInputInitialization()
@@ -187,6 +195,7 @@ void JFunctionCapillaryPressure::initializePreSubGroups()
       ? true   // pc on the gas phase, function must be increasing
       : false; // pc on the water phase, function must be decreasing
     TableCapillaryPressureHelpers::validateCapillaryPressureTable( jFuncTable, getFullName(), jFuncMustBeIncreasing );
+
   }
   else if( numPhases == 3 )
   {
@@ -205,6 +214,7 @@ void JFunctionCapillaryPressure::initializePreSubGroups()
                    InputError, getDataContext() );
     TableFunction const & jFuncTableNWI = functionManager.getGroup< TableFunction >( m_nonWettingIntermediateJFuncTableName );
     TableCapillaryPressureHelpers::validateCapillaryPressureTable( jFuncTableNWI, getFullName(), true );
+
   }
 }
 
@@ -300,11 +310,48 @@ void JFunctionCapillaryPressure::createAllTableKernelWrappers()
   // we want to make sure that the wrappers are always up-to-date, so we recreate them everytime
 
   m_jFuncKernelWrappers.clear();
+  m_inverseJFuncKernelWrappers.clear();
+
   if( numPhases == 2 )
   {
+
     TableFunction const & jFuncTable = functionManager.getGroup< TableFunction >( m_wettingNonWettingJFuncTableName );
     m_jFuncKernelWrappers.emplace_back( jFuncTable.createKernelWrapper() );
 
+    auto const & satArrayView = jFuncTable.getCoordinates()[0];
+    auto const & jArrayView   = jFuncTable.getValues();
+
+    std::vector< real64 > satVec( satArrayView.size() );
+    std::vector< real64 > jVec( jArrayView.size() );
+
+    std::copy( satArrayView.begin(), satArrayView.end(), satVec.begin() );
+    std::copy( jArrayView.begin(), jArrayView.end(), jVec.begin() );
+
+    // Reverse both arrays (if original J is decreasing in S)
+    std::reverse( jVec.begin(), jVec.end() );
+    std::reverse( satVec.begin(), satVec.end() );
+
+
+    auto inverseTable = std::make_shared< TableFunction >( "inverseJFunc", this );
+
+    real64_array invJVec( jVec.size() );
+    real64_array invSatVec( satVec.size() );
+    std::copy( jVec.begin(), jVec.end(), invJVec.data() );
+    std::copy( satVec.begin(), satVec.end(), invSatVec.data() );
+
+    array1d< real64_array > coordinates;
+    coordinates.emplace_back( std::move( invJVec ) );
+
+
+    std::vector< units::Unit > dimUnits = { units::Unknown }; // or actual unit if available
+
+    inverseTable->setTableCoordinates( coordinates, dimUnits );
+    inverseTable->setTableValues( std::move( invSatVec ), units::Unknown );
+    inverseTable->setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+    m_inverseJFuncKernelWrappers.emplace_back( inverseTable->createKernelWrapper() );
+    m_inverseTables.emplace_back( std::move( inverseTable ) );
+
     // Populate the end-points from the tables
     TableCapillaryPressureHelpers::populateMinPhaseVolumeFraction( m_phaseOrder.toSliceConst(), jFuncTable, m_phaseMinVolumeFraction );
   }
@@ -313,8 +360,10 @@ void JFunctionCapillaryPressure::createAllTableKernelWrappers()
     // the assumption used everywhere in this class is that the WI information comes before the NWI information
     TableFunction const & jFuncTableWI = functionManager.getGroup< TableFunction >( m_wettingIntermediateJFuncTableName );
     m_jFuncKernelWrappers.emplace_back( jFuncTableWI.createKernelWrapper() );
+    m_inverseJFuncKernelWrappers.emplace_back( jFuncTableWI.createKernelWrapper() );
     TableFunction const & jFuncTableNWI = functionManager.getGroup< TableFunction >( m_nonWettingIntermediateJFuncTableName );
     m_jFuncKernelWrappers.emplace_back( jFuncTableNWI.createKernelWrapper() );
+    m_inverseJFuncKernelWrappers.emplace_back( jFuncTableNWI.createKernelWrapper() );
 
     // Populate the end-points from the tables
     TableCapillaryPressureHelpers::populateMinPhaseVolumeFraction( m_phaseOrder.toSliceConst(), jFuncTableWI, jFuncTableNWI, m_phaseMinVolumeFraction );
@@ -323,6 +372,7 @@ void JFunctionCapillaryPressure::createAllTableKernelWrappers()
 
 JFunctionCapillaryPressure::KernelWrapper::
   KernelWrapper( arrayView1d< TableFunction::KernelWrapper const > const & jFuncKernelWrappers,
+                 arrayView1d< TableFunction::KernelWrapper const > const & inverseJFuncKernelWrappers,
                  arrayView2d< real64 const > const & jFuncMultiplier,
                  arrayView1d< integer const > const & phaseTypes,
                  arrayView1d< integer const > const & phaseOrder,
@@ -333,6 +383,7 @@ JFunctionCapillaryPressure::KernelWrapper::
                                  phaseCapPres,
                                  dPhaseCapPres_dPhaseVolFrac ),
   m_jFuncKernelWrappers( jFuncKernelWrappers ),
+  m_inverseJFuncKernelWrappers( inverseJFuncKernelWrappers ),
   m_jFuncMultiplier( jFuncMultiplier )
 {}
 
@@ -341,6 +392,7 @@ JFunctionCapillaryPressure::createKernelWrapper()
 {
   createAllTableKernelWrappers();
   return KernelWrapper( m_jFuncKernelWrappers,
+                        m_inverseJFuncKernelWrappers,
                         m_jFuncMultiplier,
                         m_phaseTypes,
                         m_phaseOrder,
diff --git a/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp b/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp
index 4e42189d92e..5e2f885cbf6 100644
--- a/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp
@@ -65,6 +65,7 @@ class JFunctionCapillaryPressure : public CapillaryPressureBase
 public:
 
     KernelWrapper( arrayView1d< TableFunction::KernelWrapper const > const & jFuncKernelWrappers,
+                   arrayView1d< TableFunction::KernelWrapper const > const & inverseJFuncKernelWrappers,
                    arrayView2d< real64 const > const & jFuncMultiplier,
                    arrayView1d< integer const > const & phaseTypes,
                    arrayView1d< integer const > const & phaseOrder,
@@ -77,6 +78,13 @@ class JFunctionCapillaryPressure : public CapillaryPressureBase
                   arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
                   arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
 
+    GEOS_HOST_DEVICE
+    void computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+                     arraySlice1d< real64 const > const & jFuncMultiplier,
+                     arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+                     arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
+
+
     GEOS_HOST_DEVICE
     virtual void update( localIndex const k,
                          localIndex const q,
@@ -87,6 +95,7 @@ class JFunctionCapillaryPressure : public CapillaryPressureBase
     /// Array of kernel wrappers for the J-function
     /// Is of size 1 for two-phase flow, and of size 2 for three-phase flow
     arrayView1d< TableFunction::KernelWrapper const > const m_jFuncKernelWrappers;
+    arrayView1d< TableFunction::KernelWrapper const > const m_inverseJFuncKernelWrappers;
 
     /// Array of cell-wise J-function multipliers
     /// The second dimension is of size 1 for two-phase flow, and of size 2 for three-phase flow
@@ -112,6 +121,8 @@ class JFunctionCapillaryPressure : public CapillaryPressureBase
     static constexpr char const * porosityExponentString() { return "porosityExponent"; }
     static constexpr char const * permeabilityExponentString() { return "permeabilityExponent"; }
     static constexpr char const * permeabilityDirectionString() { return "permeabilityDirection"; }
+    static constexpr char const * jFunctionWrappersString() { return "jFunctionWrappers"; }
+    static constexpr char const * inverseJFunctionWrappersString() { return "inverseJFunctionWrappers"; }
   };
 
   /**
@@ -168,6 +179,9 @@ class JFunctionCapillaryPressure : public CapillaryPressureBase
 
   /// J-function kernel wrapper for the first pair (wetting-intermediate if NP=3, wetting-non-wetting otherwise)
   array1d< TableFunction::KernelWrapper > m_jFuncKernelWrappers;
+  array1d< TableFunction::KernelWrapper > m_inverseJFuncKernelWrappers;
+
+  std::vector< std::shared_ptr< TableFunction > > m_inverseTables;
 
 };
 
@@ -242,6 +256,42 @@ JFunctionCapillaryPressure::KernelWrapper::
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+JFunctionCapillaryPressure::KernelWrapper::
+  computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+              arraySlice1d< real64 const > const & jFuncMultiplier,
+              arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+              arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const
+{
+  LvArray::forValuesInSlice( dPhaseCapPres_dPhaseVolFrac, []( real64 & val ){ val = 0.0; } );
+
+  using PT = CapillaryPressureBase::PhaseType;
+  integer const ipWater = m_phaseOrder[PT::WATER];
+  integer const ipOil   = m_phaseOrder[PT::OIL];
+  integer const ipGas   = m_phaseOrder[PT::GAS];
+
+  GEOS_UNUSED_VAR( ipOil );
+  // apply multiplier
+  real64 capPresWater_J = phaseCapPres[ipWater] / jFuncMultiplier[0];
+  // std::cout << GEOS_FMT( "        JM_2 = ( {:4.2e} )", jFuncMultiplier[0] );
+  array1d< real64 > input( 1 );
+  input[0] = capPresWater_J;
+  // std::cout << GEOS_FMT( "        J_int2 = ( {:4.2e} )", input[0] );
+  // std::cout << GEOS_FMT( "        Pc_int2 = ( {:4.2e} )", phaseCapPres[ipWater] );
+  auto inputSlice = input.toSliceConst();
+
+
+
+  phaseVolFraction[ipWater] =
+    m_inverseJFuncKernelWrappers[0].compute( inputSlice,
+                                             &(dPhaseCapPres_dPhaseVolFrac)[ipWater][ipWater] );
+  dPhaseCapPres_dPhaseVolFrac[ipWater][ipWater] /= jFuncMultiplier[0];
+  // std::cout << GEOS_FMT( "        S_int2 = ( {:4.2e} )", phaseVolFraction[ipWater] );
+  // std::cout << GEOS_FMT( "        dS/dP = ( {:4.2e} )", dPhaseCapPres_dPhaseVolFrac[ipWater][ipWater] );
+  phaseVolFraction[ipGas] = 1.0 - phaseVolFraction[ipWater];
+}
+
 GEOS_HOST_DEVICE
 inline void
 JFunctionCapillaryPressure::KernelWrapper::
diff --git a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.cpp b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.cpp
index 17b94f4730f..b925627ff4b 100644
--- a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.cpp
+++ b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.cpp
@@ -69,6 +69,10 @@ TableCapillaryPressure::TableCapillaryPressure( std::string const & name,
   registerWrapper( viewKeyStruct::capPresWrappersString(), &m_capPresKernelWrappers ).
     setSizedFromParent( 0 ).
     setRestartFlags( RestartFlags::NO_WRITE );
+
+  registerWrapper( viewKeyStruct::inverseCapPresWrappersString(), &m_inverseCapPresWrappers ).
+    setSizedFromParent( 0 ).
+    setRestartFlags( RestartFlags::NO_WRITE );
 }
 
 void TableCapillaryPressure::postInputInitialization()
@@ -154,11 +158,47 @@ void TableCapillaryPressure::createAllTableKernelWrappers()
   // we want to make sure that the wrappers are always up-to-date, so we recreate them everytime
 
   m_capPresKernelWrappers.clear();
+  m_inverseCapPresWrappers.clear();
+
   if( numPhases == 2 )
   {
     TableFunction const & capPresTable = functionManager.getGroup< TableFunction >( m_wettingNonWettingCapPresTableName );
     m_capPresKernelWrappers.emplace_back( capPresTable.createKernelWrapper() );
 
+    auto const & satArrayView = capPresTable.getCoordinates()[0];
+    auto const & capPresArrayView   = capPresTable.getValues();
+
+    std::vector< real64 > satVec( satArrayView.size() );
+    std::vector< real64 > pcVec( capPresArrayView.size() );
+
+    std::copy( satArrayView.begin(), satArrayView.end(), satVec.begin() );
+    std::copy( capPresArrayView.begin(), capPresArrayView.end(), pcVec.begin() );
+
+    // Reverse both arrays (if original J is decreasing in S)
+    std::reverse( pcVec.begin(), pcVec.end() );
+    std::reverse( satVec.begin(), satVec.end() );
+
+
+    auto inverseTable = std::make_shared< TableFunction >( "inverseCapPres", this );
+
+    real64_array invPcVec( pcVec.size() );
+    real64_array invSatVec( satVec.size() );
+    std::copy( pcVec.begin(), pcVec.end(), invPcVec.data() );
+    std::copy( satVec.begin(), satVec.end(), invSatVec.data() );
+
+    array1d< real64_array > coordinates;
+    coordinates.emplace_back( std::move( invPcVec ) );
+
+
+    std::vector< units::Unit > dimUnits = { units::Unknown }; // or actual unit if available
+
+    inverseTable->setTableCoordinates( coordinates, dimUnits );
+    inverseTable->setTableValues( std::move( invSatVec ), units::Unknown );
+    inverseTable->setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+    m_inverseCapPresWrappers.emplace_back( inverseTable->createKernelWrapper() );
+    m_inverseTables.emplace_back( std::move( inverseTable ) );
+
     // Populate the end-points from the tables
     TableCapillaryPressureHelpers::populateMinPhaseVolumeFraction( m_phaseOrder.toSliceConst(), capPresTable, m_phaseMinVolumeFraction );
   }
@@ -166,8 +206,10 @@ void TableCapillaryPressure::createAllTableKernelWrappers()
   {
     TableFunction const & capPresTableWI = functionManager.getGroup< TableFunction >( m_wettingIntermediateCapPresTableName );
     m_capPresKernelWrappers.emplace_back( capPresTableWI.createKernelWrapper() );
+    m_inverseCapPresWrappers.emplace_back( capPresTableWI.createKernelWrapper() );
     TableFunction const & capPresTableNWI = functionManager.getGroup< TableFunction >( m_nonWettingIntermediateCapPresTableName );
     m_capPresKernelWrappers.emplace_back( capPresTableNWI.createKernelWrapper() );
+    m_inverseCapPresWrappers.emplace_back( capPresTableNWI.createKernelWrapper() );
 
     // Populate the end-points from the tables
     TableCapillaryPressureHelpers::populateMinPhaseVolumeFraction( m_phaseOrder.toSliceConst(), capPresTableWI, capPresTableNWI, m_phaseMinVolumeFraction );
@@ -177,6 +219,7 @@ void TableCapillaryPressure::createAllTableKernelWrappers()
 
 TableCapillaryPressure::KernelWrapper::
   KernelWrapper( arrayView1d< TableFunction::KernelWrapper const > const & capPresKernelWrappers,
+                 arrayView1d< TableFunction::KernelWrapper const > const & inverseCapPresWrappers,
                  arrayView1d< integer const > const & phaseTypes,
                  arrayView1d< integer const > const & phaseOrder,
                  arrayView3d< real64, cappres::USD_CAPPRES > const & phaseCapPres,
@@ -185,7 +228,8 @@ TableCapillaryPressure::KernelWrapper::
                                  phaseOrder,
                                  phaseCapPres,
                                  dPhaseCapPres_dPhaseVolFrac ),
-  m_capPresKernelWrappers( capPresKernelWrappers )
+  m_capPresKernelWrappers( capPresKernelWrappers ),
+  m_inverseCapPresWrappers( inverseCapPresWrappers )
 {}
 
 TableCapillaryPressure::KernelWrapper
@@ -193,6 +237,7 @@ TableCapillaryPressure::createKernelWrapper()
 {
   createAllTableKernelWrappers();
   return KernelWrapper( m_capPresKernelWrappers,
+                        m_inverseCapPresWrappers,
                         m_phaseTypes,
                         m_phaseOrder,
                         m_phaseCapPressure,
diff --git a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.hpp b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.hpp
index 739b9993083..5d132d3636a 100644
--- a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.hpp
@@ -55,6 +55,7 @@ class TableCapillaryPressure : public CapillaryPressureBase
 public:
 
     KernelWrapper( arrayView1d< TableFunction::KernelWrapper const > const & capPresKernelWrappers,
+                   arrayView1d< TableFunction::KernelWrapper const > const & inverseCapPresWrappers,
                    arrayView1d< integer const > const & phaseTypes,
                    arrayView1d< integer const > const & phaseOrder,
                    arrayView3d< real64, cappres::USD_CAPPRES > const & phaseCapPres,
@@ -65,6 +66,12 @@ class TableCapillaryPressure : public CapillaryPressureBase
                   arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
                   arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
 
+    GEOS_HOST_DEVICE
+    void computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+                     arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+                     arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
+
+
     GEOS_HOST_DEVICE
     virtual void update( localIndex const k,
                          localIndex const q,
@@ -75,6 +82,7 @@ class TableCapillaryPressure : public CapillaryPressureBase
     /// Array of kernel wrappers for the capillary pressures
     /// Is of size 1 for two-phase flow, and of size 2 for three-phase flow
     arrayView1d< TableFunction::KernelWrapper const > const m_capPresKernelWrappers;
+    arrayView1d< TableFunction::KernelWrapper const > const m_inverseCapPresWrappers;
 
   };
 
@@ -91,6 +99,7 @@ class TableCapillaryPressure : public CapillaryPressureBase
     static constexpr char const * wettingIntermediateCapPresTableNameString() { return "wettingIntermediateCapPressureTableName"; }
     static constexpr char const * nonWettingIntermediateCapPresTableNameString() { return "nonWettingIntermediateCapPressureTableName"; }
     static constexpr char const * capPresWrappersString() { return "capPresWrappers"; }
+    static constexpr char const * inverseCapPresWrappersString() { return "inverseCapPresWrappers"; }
 
   };
 
@@ -116,6 +125,9 @@ class TableCapillaryPressure : public CapillaryPressureBase
 
   /// Capillary pressure kernel wrapper for the first pair (wetting-intermediate if NP=3, wetting-non-wetting otherwise)
   array1d< TableFunction::KernelWrapper > m_capPresKernelWrappers;
+  array1d< TableFunction::KernelWrapper > m_inverseCapPresWrappers;
+
+  std::vector< std::shared_ptr< TableFunction > > m_inverseTables;
 
 };
 
@@ -173,6 +185,39 @@ TableCapillaryPressure::KernelWrapper::
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+TableCapillaryPressure::KernelWrapper::
+  computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+              arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+              arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const
+{
+  LvArray::forValuesInSlice( dPhaseCapPres_dPhaseVolFrac, []( real64 & val ){ val = 0.0; } );
+
+  using PT = CapillaryPressureBase::PhaseType;
+  integer const ipWater = m_phaseOrder[PT::WATER];
+  integer const ipOil   = m_phaseOrder[PT::OIL];
+  integer const ipGas   = m_phaseOrder[PT::GAS];
+
+  GEOS_UNUSED_VAR( ipOil );
+
+  // put capillary pressure on the wetting phase
+  real64 capPresWater = phaseCapPres[ipWater];
+  array1d< real64 > input( 1 );
+  input[0] = capPresWater;
+  auto inputSlice = input.toSliceConst();
+
+  phaseVolFraction[ipWater] =
+    m_capPresKernelWrappers[0].compute( &(phaseCapPres)[ipWater],
+                                        &(dPhaseCapPres_dPhaseVolFrac)[ipWater][ipWater] );
+  phaseVolFraction[ipWater] =
+    m_inverseCapPresWrappers[0].compute( inputSlice,
+                                         &(dPhaseCapPres_dPhaseVolFrac)[ipWater][ipWater] );
+  phaseVolFraction[ipGas] = 1.0 - phaseVolFraction[ipWater];
+
+}
+
+
 GEOS_HOST_DEVICE
 inline void
 TableCapillaryPressure::KernelWrapper::
diff --git a/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.hpp b/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.hpp
index f3af8198d60..6ac95221027 100644
--- a/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.hpp
@@ -57,6 +57,11 @@ class VanGenuchtenCapillaryPressureUpdate final : public CapillaryPressureBaseUp
                 arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
                 arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
 
+  GEOS_HOST_DEVICE
+  void computeInv( arraySlice1d< real64 const, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+                   arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+                   arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
+
   GEOS_HOST_DEVICE
   virtual void update( localIndex const k,
                        localIndex const q,
@@ -189,6 +194,69 @@ VanGenuchtenCapillaryPressureUpdate::
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+VanGenuchtenCapillaryPressureUpdate::
+  computeInv( arraySlice1d< real64 const, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+              arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+              arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const
+{
+  LvArray::forValuesInSlice( dPhaseCapPres_dPhaseVolFrac, []( real64 & val ){ val = 0.0; } );
+
+  // the VanGenuchten model does not support volFracScaled = 0 and = 1
+  // hence we need an epsilon value to avoid a division by zero
+  // TODO: for S < epsilon and S > 1 - epsilon, replace the original unbounded VG curve with a bounded power-law
+  // extension
+  real64 const eps = m_capPressureEpsilon;
+  real64 const volFracScaleInv = 1.0 / m_volFracScale;
+
+  // compute first water-oil capillary pressure as a function of water-phase vol fraction
+  integer const ip_water = m_phaseOrder[CapillaryPressureBase::PhaseType::WATER];
+  if( ip_water >= 0 )
+  {
+
+    real64 const volFracScaled = (phaseVolFraction[ip_water] - m_phaseMinVolumeFraction[ip_water]) * volFracScaleInv;
+    real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_water]; // div by 0 taken care of by initialization
+                                                                          // check
+    real64 const multiplier    = m_phaseCapPressureMultiplier[ip_water];
+
+    real64 const scaledWettingVolFrac                = volFracScaled;
+    real64 const dScaledWettingPhaseVolFrac_dVolFrac = volFracScaleInv;
+
+    evaluateVanGenuchtenFunction( scaledWettingVolFrac,
+                                  dScaledWettingPhaseVolFrac_dVolFrac,
+                                  exponentInv,
+                                  multiplier,
+                                  eps,
+                                  phaseCapPres[ip_water],
+                                  dPhaseCapPres_dPhaseVolFrac[ip_water][ip_water] );
+
+  }
+
+
+  // then compute the oil-gas capillary pressure as a function of gas-phase vol fraction
+  integer const ip_gas = m_phaseOrder[CapillaryPressureBase::PhaseType::GAS];
+  if( ip_gas >= 0 )
+  {
+    real64 const volFracScaled = (phaseVolFraction[ip_gas] - m_phaseMinVolumeFraction[ip_gas]) * volFracScaleInv;
+    real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_gas]; // div by 0 taken care of by initialization
+                                                                        // check
+    real64 const multiplier    = -m_phaseCapPressureMultiplier[ip_gas]; // for gas capillary pressure, take the opposite
+                                                                        // of the VG function
+
+    real64 const scaledWettingVolFrac                = 1-volFracScaled;
+    real64 const dScaledWettingPhaseVolFrac_dVolFrac =  -volFracScaleInv;
+
+    evaluateVanGenuchtenFunction( scaledWettingVolFrac,
+                                  dScaledWettingPhaseVolFrac_dVolFrac,
+                                  exponentInv,
+                                  multiplier,
+                                  eps,
+                                  phaseCapPres[ip_gas],
+                                  dPhaseCapPres_dPhaseVolFrac[ip_gas][ip_gas] );
+  }
+}
+
 GEOS_HOST_DEVICE
 GEOS_FORCE_INLINE
 void
diff --git a/src/coreComponents/constitutive/docs/TwoPhaseFluid.rst b/src/coreComponents/constitutive/docs/TwoPhaseFluid.rst
new file mode 100644
index 00000000000..39b35510c63
--- /dev/null
+++ b/src/coreComponents/constitutive/docs/TwoPhaseFluid.rst
@@ -0,0 +1,90 @@
+.. _TwoPhaseFluid:
+
+############################################
+Two-phase fluid model
+############################################
+
+Overview
+=========================
+
+This model represents a two-phase fluid with pressure-dependent density and viscosity.
+
+For each phase, both density and viscosity are described as tabulated data, either in the form of ``TableFunction`` or text files.
+
+In the case of text files, one file is expected per phase and should consist of three columns: pressure, density and viscosity.
+
+Note that currently, there is no temperature dependence in the model.
+
+
+Parameters
+=========================
+
+The model is represented by ``<TwoPhaseFluid>`` node in the input.
+
+The following attributes are supported:
+
+.. include:: /docs/sphinx/datastructure/TwoPhaseFluid.rst
+              
+
+Example using TableFunctions
+============================
+
+.. code-block:: xml
+
+  <Constitutive>
+    <TwoPhaseFluid
+      name="fluid"
+      phaseNames="{ oil, water }"
+      densityTableNames="{ densityTableOil, densityTableWater }"
+      viscosityTableNames="{ viscosityTableOil, viscosityTableWater }" />
+  </Constitutive>
+
+  <Functions>
+    <TableFunction
+      name="densityTableOil"
+      coordinateFiles="{ pres_pvdo.txt }"
+      voxelFile="dens_pvdo.txt"
+      interpolation="linear" />
+
+    <TableFunction
+      name="viscosityTableOil"
+      coordinateFiles="{ pres_pvdo.txt }"
+      voxelFile="visc_pvdo.txt"
+      interpolation="linear" />
+
+    <TableFunction
+      name="densityTableWater"
+      coordinates="{ 2068000, 5516000, 30600000, 55160000 }"
+      values="{ 980.683, 982.07, 992.233, 1002.265 }"
+      interpolation="linear" />
+
+    <TableFunction
+      name="viscosityTableWater"
+      coordinates="{ 0 }"
+      values="{ 0.0003 }"
+      interpolation="linear" />
+  </Functions>  
+
+
+Example using text files
+=========================
+
+.. code-block:: xml
+
+  <Constitutive>
+    <TwoPhaseFluid
+      name="fluid"
+      phaseNames="{ oil, water }"
+      tableNames="{ oil.txt, water.txt }" />
+  </Constitutive>
+
+
+with, for example, ``water.txt`` being set as:
+
+.. code-block:: text
+
+  #  P(Pa) Dens(kg/m3) Visc(Pa.s)
+   2068000     980.683     0.0003     
+   5516000      982.07     0.0003
+  30600000     992.233     0.0003
+  55160000    1002.265     0.0003
diff --git a/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.cpp b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.cpp
new file mode 100644
index 00000000000..ad6379ea129
--- /dev/null
+++ b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.cpp
@@ -0,0 +1,268 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 Total, S.A
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+/**
+ * @file TwoPhaseFluid.cpp
+ */
+
+#include "constitutive/fluid/multifluid/CO2Brine/functions/PVTFunctionHelpers.hpp" // for readTable
+#include "TwoPhaseFluid.hpp"
+#include "TwoPhaseFluidFields.hpp"
+
+#include "functions/FunctionManager.hpp"
+
+
+namespace geos
+{
+
+using namespace dataRepository;
+
+namespace constitutive
+{
+
+
+TwoPhaseFluid::TwoPhaseFluid( string const & name, Group * const parent )
+  : ConstitutiveBase( name, parent )
+{
+  registerWrapper( viewKeyStruct::phaseNamesString(), &m_phaseNames ).
+    setRTTypeName( rtTypes::CustomTypes::groupNameRefArray ).
+    setInputFlag( InputFlags::OPTIONAL ).
+    setDescription( "List of fluid phases" );
+
+  // 1) First option: specify PVT tables from one file per phase, read the files line by line, and populate the internal TableFunctions
+  registerWrapper( viewKeyStruct::tableFilesString(), &m_tableFiles ).
+    setInputFlag( InputFlags::OPTIONAL ).
+    setRestartFlags( RestartFlags::NO_WRITE ).
+    setDescription( "List of filenames with input PVT tables (one per phase)" );
+
+  // 2) Second option: specify TableFunction names for each phase,
+  registerWrapper( viewKeyStruct::densityTableNamesString(), &m_densityTableNames ).
+    setRTTypeName( rtTypes::CustomTypes::groupNameRefArray ).
+    setInputFlag( InputFlags::OPTIONAL ).
+    setDescription( "List of density TableFuncion names from the Function block. \n"
+                    "The user must provide one TableFunction per phase, respecting the order provided in \"phaseNames\"." );
+
+  registerWrapper( viewKeyStruct::viscosityTableNamesString(), &m_viscosityTableNames ).
+    setRTTypeName( rtTypes::CustomTypes::groupNameRefArray ).
+    setInputFlag( InputFlags::OPTIONAL ).
+    setDescription( "List of viscosity TableFuncion names from the Function block. \n"
+                    "The user must provide one TableFunction per phase, respecting the order provided in \"phaseNames\"." );
+
+  registerField( fields::twophasefluid::phaseDensity{}, &m_phaseDensity.value );
+  registerField( fields::twophasefluid::dPhaseDensity{}, &m_phaseDensity.derivs );
+  registerField( fields::twophasefluid::phaseDensity_n{}, &m_phaseDensity_n );
+
+  registerField( fields::twophasefluid::phaseViscosity{}, &m_phaseViscosity.value );
+  registerField( fields::twophasefluid::dPhaseViscosity{}, &m_phaseViscosity.derivs );
+}
+
+
+std::unique_ptr< ConstitutiveBase >
+TwoPhaseFluid::deliverClone( string const & name, Group * const parent ) const
+{
+  return ConstitutiveBase::deliverClone( name, parent );
+}
+
+
+void TwoPhaseFluid::resizeFields( localIndex const size, localIndex const numPts )
+{
+  // Assume sole dependency on pressure, i.e. one derivative
+  m_phaseDensity.value.resize( size, numPts, 2 );
+  m_phaseDensity.derivs.resize( size, numPts, 2, 1 );
+
+  m_phaseDensity_n.resize( size, numPts, 2 );
+
+  m_phaseViscosity.value.resize( size, numPts, 2 );
+  m_phaseViscosity.derivs.resize( size, numPts, 2, 1 );
+}
+
+
+void TwoPhaseFluid::allocateConstitutiveData( dataRepository::Group & parent,
+                                              localIndex const numConstitutivePointsPerParentIndex )
+{
+  ConstitutiveBase::allocateConstitutiveData( parent, numConstitutivePointsPerParentIndex );
+  resizeFields( parent.size(), numConstitutivePointsPerParentIndex );
+}
+
+
+void TwoPhaseFluid::postInputInitialization()
+{
+  ConstitutiveBase::postInputInitialization();
+
+  // Input relationships can be provided either as text files or TableFunctions.
+  m_tableFiles.empty() ? readInputDataFromTableFunctions() : readInputDataFromFileTableFunctions();
+
+  checkTableConsistency();
+}
+
+
+void TwoPhaseFluid::fillData( integer const ip,
+                              array1d< array1d< real64 > > const & tableValues )
+{
+  array1d< array1d< real64 > > pressureCoords( 1 );
+  pressureCoords[0].resize( tableValues.size() );
+  array1d< real64 > density( tableValues.size() );
+  array1d< real64 > viscosity( tableValues.size() );
+
+  for( localIndex i = 0; i < tableValues.size(); ++i )
+  {
+    GEOS_THROW_IF_NE_MSG( tableValues[i].size(), 3,
+                          GEOS_FMT( "{}: three columns (pressure, density, and viscosity) are expected", getFullName() ),
+                          InputError );
+
+    pressureCoords[0][i] = tableValues[i][0];
+    density[i] = tableValues[i][1];
+    viscosity[i] = tableValues[i][2];
+  }
+
+  string const densityTableName = getName() + "DensityPhase" + GEOS_FMT( "{}", ip );
+  string const viscosityTableName = getName() +  "ViscosityPhase" + GEOS_FMT( "{}", ip );
+  m_densityTableNames.emplace_back( densityTableName );
+  m_viscosityTableNames.emplace_back( viscosityTableName );
+
+  FunctionManager & functionManager = FunctionManager::getInstance();
+
+  TableFunction & tableDensity =
+    dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", densityTableName ) );
+  tableDensity.setTableCoordinates( pressureCoords, { units::Pressure } );
+  tableDensity.setTableValues( density, units::Density );
+  tableDensity.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  TableFunction & tableViscosity =
+    dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", viscosityTableName ) );
+  tableViscosity.setTableCoordinates( pressureCoords, { units::Pressure } );
+  tableViscosity.setTableValues( viscosity, units::Viscosity );
+  tableViscosity.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+}
+
+
+void TwoPhaseFluid::readInputDataFromFileTableFunctions()
+{
+  // Check for ambiguous definition
+  GEOS_THROW_IF( !(m_densityTableNames.empty() && m_viscosityTableNames.empty()),
+                 GEOS_FMT( "{}: input is redundant (both TableFunction names and text files)", getFullName() ),
+                 InputError );
+
+
+  // Check that we have exactly two table files (one per phase)
+  GEOS_THROW_IF_NE_MSG( m_tableFiles.size(), 2,
+                        GEOS_FMT( "{}: expecting two table files (one per phase)", getFullName() ),
+                        InputError );
+
+  array1d< array1d< real64 > > tableValues;
+  for( integer ip = 0; ip < 2; ++ip )
+  {
+    tableValues.clear();
+    geos::constitutive::PVTProps::BlackOilTables::readTable( m_tableFiles[ip], 3, tableValues );
+    fillData( ip, tableValues );
+  }
+}
+
+
+void TwoPhaseFluid::readInputDataFromTableFunctions()
+{
+  // Check for ambiguous definition
+  GEOS_THROW_IF( !m_tableFiles.empty(),
+                 GEOS_FMT( "{}: input is redundant (both TableFunction names and text files)", getFullName() ),
+                 InputError );
+
+  // Since we are considering a two phase fluid, we should have exactly 2 tables per property
+  GEOS_THROW_IF_NE_MSG( m_densityTableNames.size(), 2,
+                        GEOS_FMT( "{}: one density table must be provided for each phase", getFullName() ),
+                        InputError );
+
+  GEOS_THROW_IF_NE_MSG( m_viscosityTableNames.size(), 2,
+                        GEOS_FMT( "{}: one viscosity table must be provided for each phase", getFullName() ),
+                        InputError );
+
+
+  FunctionManager const & functionManager = FunctionManager::getInstance();
+
+  for( integer iph = 0; iph < 2; ++iph )
+  {
+    GEOS_THROW_IF( !functionManager.hasGroup( m_densityTableNames[iph] ),
+                   GEOS_FMT( "{}: density table '{}' not found", getFullName(), m_densityTableNames[iph] ),
+                   InputError );
+
+    GEOS_THROW_IF( !functionManager.hasGroup( m_viscosityTableNames[iph] ),
+                   GEOS_FMT( "{}: viscosity table '{}' not found", getFullName(), m_viscosityTableNames[iph] ),
+                   InputError );
+  }
+}
+
+
+void TwoPhaseFluid::initializePostSubGroups()
+{
+  ConstitutiveBase::initializePostSubGroups();
+
+  FunctionManager const & functionManager = FunctionManager::getInstance();
+  for( integer iph = 0; iph < 2; ++iph )
+  {
+    // Grab the tables by name from the function manager,
+    // then add them in a list to create their table wrappers when needed
+    TableFunction const & densityTable = functionManager.getGroup< TableFunction const >( m_densityTableNames[iph] );
+    m_densityTables.emplace_back( &densityTable );
+    m_densityTableKernels.emplace_back( m_densityTables[iph]->createKernelWrapper() );
+
+    TableFunction const & viscosityTable = functionManager.getGroup< TableFunction const >( m_viscosityTableNames[iph] );
+    m_viscosityTables.emplace_back( &viscosityTable );
+    m_viscosityTableKernels.emplace_back( m_viscosityTables[iph]->createKernelWrapper() );
+  }
+}
+
+
+void TwoPhaseFluid::checkTableConsistency() const
+{
+  FunctionManager const & functionManager = FunctionManager::getInstance();
+  for( integer iph = 0; iph < 2; ++iph )
+  {
+    TableFunction const & densityTable = functionManager.getGroup< TableFunction const >( m_densityTableNames[iph] );
+    arrayView1d< real64 const > const density = densityTable.getValues();
+
+    for( localIndex i = 1; i < density.size(); ++i )
+    {
+      GEOS_THROW_IF( density[i] - density[i-1] < 0,
+                     GEOS_FMT( "{}: in table '{}' density values must be increasing", getFullName(), densityTable.getName() ),
+                     InputError );
+    }
+  }
+}
+
+
+TwoPhaseFluid::KernelWrapper
+TwoPhaseFluid::createKernelWrapper()
+{
+  return KernelWrapper( m_densityTableKernels,
+                        m_viscosityTableKernels,
+                        m_phaseDensity.toView(),
+                        m_phaseViscosity.toView());
+}
+
+
+TwoPhaseFluid::KernelWrapper::KernelWrapper(
+  arrayView1d< TableFunction::KernelWrapper const > densityTables,
+  arrayView1d< TableFunction::KernelWrapper const > viscosityTables,
+  PhaseProp::ViewType phaseDensity,
+  PhaseProp::ViewType phaseViscosity )
+  : m_densityTables( std::move( densityTables )),
+  m_viscosityTables( std::move( viscosityTables )),
+  m_phaseDensity( std::move( phaseDensity )),
+  m_phaseViscosity( std::move( phaseViscosity )) {}
+
+
+REGISTER_CATALOG_ENTRY( ConstitutiveBase, TwoPhaseFluid, string const &, Group * const )
+
+}  // namespace constitutive
+}  // namespace geos
diff --git a/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.hpp b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.hpp
new file mode 100644
index 00000000000..18cdc357bb0
--- /dev/null
+++ b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.hpp
@@ -0,0 +1,344 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 Total, S.A
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+/**
+ * @file TwoPhaseFluid.hpp
+ */
+
+#ifndef GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUID_TWOPHASEFLUID_HPP_
+#define GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUID_TWOPHASEFLUID_HPP_
+
+#include "common/DataLayouts.hpp"
+#include "functions/TableFunction.hpp"
+#include "constitutive/ConstitutiveBase.hpp"
+
+#include "constitutive/fluid/multifluid/Layouts.hpp"
+#include "constitutive/fluid/multifluid/MultiFluidUtils.hpp"
+
+#include "constitutive/ConstitutivePassThruHandler.hpp"
+
+
+namespace geos
+{
+namespace constitutive
+{
+
+class TwoPhaseFluid : public ConstitutiveBase
+{
+public:
+
+  TwoPhaseFluid( string const & name,
+                 Group * const parent );
+
+  virtual std::unique_ptr< ConstitutiveBase >
+  deliverClone( string const & name,
+                Group * const parent ) const override;
+
+  virtual void allocateConstitutiveData( dataRepository::Group & parent,
+                                         localIndex const numConstitutivePointsPerParentIndex ) override;
+
+  /**
+   * @name Static Factory Catalog members and functions
+   */
+  ///@{
+
+  /**
+   * @brief Static catalog string
+   * @return A string that is used to register/lookup this class in the registry
+   */
+  static std::string catalogName() { return "TwoPhaseFluid"; }
+
+  /**
+   * @brief Get catalog name
+   * @return Name string
+   */
+  virtual string getCatalogName() const override { return catalogName(); }
+
+  ///@}
+
+
+
+  /**
+   * @brief Getter for the fluid phase names
+   * @return an array storing the phase names
+   */
+  string_array const & phaseNames() const { return m_phaseNames; }
+
+  struct viewKeyStruct : ConstitutiveBase::viewKeyStruct
+  {
+    static constexpr char const * tableFilesString() { return "tableFiles"; }
+    static constexpr char const * phaseNamesString() { return "phaseNames"; }
+    static constexpr char const * densityTableNamesString() { return "densityTableNames"; }
+    static constexpr char const * viscosityTableNamesString() { return "viscosityTableNames"; }
+  };
+
+  arrayView3d< real64 const, multifluid::USD_PHASE > phaseDensity_n() const
+  { return m_phaseDensity_n; }
+
+  arrayView3d< real64 const, multifluid::USD_PHASE > phaseDensity() const
+  { return m_phaseDensity.value; }
+
+  arrayView4d< real64 const, multifluid::USD_PHASE_DC > dPhaseDensity() const
+  { return m_phaseDensity.derivs; }
+
+  arrayView3d< real64 const, multifluid::USD_PHASE > phaseViscosity() const
+  { return m_phaseViscosity.value; }
+
+  arrayView4d< real64 const, multifluid::USD_PHASE_DC > dPhaseViscosity() const
+  { return m_phaseViscosity.derivs; }
+
+  using PhaseProp = MultiFluidVar< real64, 3, constitutive::multifluid::LAYOUT_PHASE, constitutive::multifluid::LAYOUT_PHASE_DC >;
+
+
+  class KernelWrapper
+  {
+public:
+
+    /// @cond DO_NOT_DOCUMENT
+    /// We need these SMFs to avoid host-device errors with CUDA.
+    KernelWrapper() = default;
+    KernelWrapper( KernelWrapper const & ) = default;
+    KernelWrapper & operator=( KernelWrapper const & ) = default;
+    KernelWrapper & operator=( KernelWrapper && ) = default;
+    /// @endcond
+
+    /**
+     * @brief Get number of elements in this wrapper.
+     * @return number of elements
+     */
+    GEOS_HOST_DEVICE
+    GEOS_FORCE_INLINE
+    localIndex numElems() const { return m_phaseDensity.value.size( 0 ); }
+
+    /**
+     * @brief Get number of gauss points per element.
+     * @return number of gauss points per element
+     */
+    GEOS_HOST_DEVICE
+    GEOS_FORCE_INLINE
+    localIndex numGauss() const { return m_phaseDensity.value.size( 1 ); }
+
+
+    GEOS_HOST_DEVICE
+    void compute( real64 const pressure,
+                  PhaseProp::SliceType const phaseDensity,
+                  PhaseProp::SliceType const phaseViscosity ) const;
+
+    GEOS_HOST_DEVICE
+    void update( localIndex const k,
+                 localIndex const q,
+                 real64 const pressure ) const;
+
+private:
+
+    friend class TwoPhaseFluid;
+
+    /**
+     * @brief Constructor for the class doing in-kernel two-phase fluid updates
+     * @param[in] densityTables density tables
+     * @param[in] viscosityTables viscosity tables
+     * @param[in] phaseDensity phase densities (+ derivatives) in the cell
+     * @param[in] phaseViscosity phase viscosities (+ derivatives) in the cell
+     */
+    KernelWrapper(
+      arrayView1d< TableFunction::KernelWrapper const > densityTables,
+      arrayView1d< TableFunction::KernelWrapper const > viscosityTables,
+      PhaseProp::ViewType phaseDensity,
+      PhaseProp::ViewType phaseViscosity );
+
+
+protected:
+
+    KernelWrapper(
+      arrayView1d< TableFunction::KernelWrapper const > densityTables,
+      arrayView1d< TableFunction::KernelWrapper const > viscosityTables
+      );
+
+    /// Table kernel wrappers to interpolate in the two phase (\rho vs p) tables
+    arrayView1d< TableFunction::KernelWrapper const > m_densityTables;
+
+    /// Table kernel wrappers to interpolate in the two phase (\mu vs p) tables
+    arrayView1d< TableFunction::KernelWrapper const > m_viscosityTables;
+
+    /**
+     * @brief Utility function to compute densities as a function of pressure (keeping derivatives)
+     * @param[in] pressure pressure in the cell
+     * @param[out] phaseDensity the phase density in the cell (+ derivatives)
+     */
+    GEOS_HOST_DEVICE
+    void computeDensities( real64 const pressure,
+                           PhaseProp::SliceType const & phaseDensity ) const;
+
+    /**
+     * @brief Utility function to compute viscosities as a function of pressure (keeping derivatives)
+     * @param[in] pressure pressure in the cell
+     * @param[out] phaseViscosity the phase viscosities in the cell (+ derivatives)
+     */
+    GEOS_HOST_DEVICE
+    void computeViscosities( real64 const pressure,
+                             PhaseProp::SliceType const & phaseViscosity ) const;
+
+    /// Views on the phase properties
+    PhaseProp::ViewType m_phaseDensity;
+    PhaseProp::ViewType m_phaseViscosity;
+
+  };  //class KernelWrapper
+
+
+  string_array m_phaseNames;
+
+
+  path_array m_tableFiles;
+
+  /// Names of the density tables (one per phase)
+  string_array m_densityTableNames;
+
+  /// Names of the viscosity tables (one per phase)
+  string_array m_viscosityTableNames;
+
+  PhaseProp m_phaseDensity;
+  PhaseProp m_phaseViscosity;
+
+  /// Backup data
+  array3d< real64, multifluid::LAYOUT_PHASE > m_phaseDensity_n;
+
+
+  virtual void resizeFields( localIndex const size, localIndex const numPts );
+
+  virtual void postInputInitialization() override;
+
+  virtual void initializePostSubGroups() override;
+
+  /// Table kernel wrappers to interpolate (\rho vs p) tables
+  array1d< TableFunction const * > m_densityTables;
+  /// Table kernel wrappers of m_densityTables
+  array1d< TableFunction::KernelWrapper > m_densityTableKernels;
+
+  /// Table kernel wrappers to interpolate (\mu vs p) tables
+  array1d< TableFunction const * > m_viscosityTables;
+  /// Table kernel wrappers of m_viscosityTables
+  array1d< TableFunction::KernelWrapper > m_viscosityTableKernels;
+
+  KernelWrapper createKernelWrapper();
+
+
+private:
+  void readInputDataFromTableFunctions();
+  void readInputDataFromFileTableFunctions();
+
+  /**
+   * @brief Fill the fluid data (pressure, density, viscosity)
+   * @param[in] ip the index of the phase
+   * @param[in] tableValues the values in the fluid table
+   */
+  void fillData( integer const ip,
+                 array1d< array1d< real64 > > const & tableValues );
+
+  /**
+   * @brief Check the monotonicity of the PVT relationship
+   */
+  void checkTableConsistency() const;
+};
+
+
+GEOS_HOST_DEVICE
+GEOS_FORCE_INLINE
+void TwoPhaseFluid::KernelWrapper::
+  computeDensities( real64 const pressure,
+                    PhaseProp::SliceType const & phaseDensity ) const
+{
+  using Deriv = constitutive::multifluid::DerivativeOffset;
+
+  LvArray::forValuesInSlice( phaseDensity.derivs, []( real64 & val ) { val = 0.0; } );
+
+  for( integer iph = 0; iph < 2; ++iph )
+  {
+    // interpolate in the table to get the phase density and derivatives
+    real64 dPhaseDens_dPres = 0.0;
+
+    phaseDensity.value[iph] = m_densityTables[iph].compute( &pressure, &dPhaseDens_dPres );
+    phaseDensity.derivs[iph][Deriv::dP] = dPhaseDens_dPres;
+  }
+}
+
+
+GEOS_HOST_DEVICE
+GEOS_FORCE_INLINE
+void TwoPhaseFluid::KernelWrapper::
+  computeViscosities( real64 const pressure,
+                      PhaseProp::SliceType const & phaseViscosity ) const
+{
+  using Deriv = constitutive::multifluid::DerivativeOffset;
+
+  LvArray::forValuesInSlice( phaseViscosity.derivs, []( real64 & val ) { val = 0.0; } );
+
+  for( integer iph = 0; iph < 2; ++iph )
+  {
+    // interpolate in the table to get the phase viscosity and derivatives
+    real64 dPhaseVisc_dPres = 0.0;
+    phaseViscosity.value[iph] = m_viscosityTables[iph].compute( &pressure, &dPhaseVisc_dPres );
+    phaseViscosity.derivs[iph][Deriv::dP] = dPhaseVisc_dPres;
+  }
+}
+
+
+GEOS_HOST_DEVICE
+GEOS_FORCE_INLINE
+void TwoPhaseFluid::KernelWrapper::
+  compute( real64 const pressure,
+           PhaseProp::SliceType const phaseDensity,
+           PhaseProp::SliceType const phaseViscosity ) const
+{
+  computeDensities( pressure,
+                    phaseDensity );
+
+  computeViscosities( pressure,
+                      phaseViscosity );
+}
+
+
+GEOS_HOST_DEVICE
+GEOS_FORCE_INLINE
+void TwoPhaseFluid::KernelWrapper::
+  update( localIndex const k,
+          localIndex const q,
+          real64 const pressure
+          ) const
+{
+  compute( pressure,
+           m_phaseDensity( k, q ),
+           m_phaseViscosity( k, q ) );
+}
+
+
+template< typename LAMBDA >
+void constitutiveUpdatePassThru( TwoPhaseFluid const & fluid,
+                                 LAMBDA && lambda )
+{
+  ConstitutivePassThruHandler< TwoPhaseFluid >::execute( fluid, std::forward< LAMBDA >( lambda ) );
+}
+
+
+template< typename LAMBDA >
+void constitutiveUpdatePassThru( TwoPhaseFluid & fluid,
+                                 LAMBDA && lambda )
+{
+  ConstitutivePassThruHandler< TwoPhaseFluid >::execute( fluid, std::forward< LAMBDA >( lambda ) );
+}
+
+}  // namespace constitutive
+}  // namespace geos
+
+#endif // GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUID_TWOPHASEFLUID_HPP_
diff --git a/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluidFields.hpp b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluidFields.hpp
new file mode 100644
index 00000000000..9ce0dc5c33d
--- /dev/null
+++ b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluidFields.hpp
@@ -0,0 +1,84 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 Total, S.A
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+/**
+ * @file TwoPhaseFluidFields.hpp
+ */
+
+#ifndef GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUIDFIELDS_HPP_
+#define GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUIDFIELDS_HPP_
+
+#include "constitutive/fluid/multifluid/Layouts.hpp"
+#include "mesh/MeshFields.hpp"
+
+
+namespace geos
+{
+
+namespace fields
+{
+
+namespace twophasefluid
+{
+
+using array3dLayoutPhase = array3d< real64, constitutive::multifluid::LAYOUT_PHASE >;
+using array4dLayoutPhase_d = array4d< real64, constitutive::multifluid::LAYOUT_PHASE_DC >;
+
+DECLARE_FIELD( phaseDensity,
+               "phaseDensity",
+               array3dLayoutPhase,
+               0,
+               LEVEL_0,
+               WRITE_AND_READ,
+               "Phase density" );
+
+DECLARE_FIELD( phaseDensity_n,
+               "phaseDensity_n",
+               array3dLayoutPhase,
+               0,
+               NOPLOT,
+               WRITE_AND_READ,
+               "Phase density at the previous converged time step" );
+
+DECLARE_FIELD( dPhaseDensity,
+               "dPhaseDensity",
+               array4dLayoutPhase_d,
+               0,
+               NOPLOT,
+               NO_WRITE,
+               "Derivative of phase density with respect to pressure" );
+
+DECLARE_FIELD( phaseViscosity,
+               "phaseViscosity",
+               array3dLayoutPhase,
+               0,
+               LEVEL_0,
+               WRITE_AND_READ,
+               "Phase viscosity" );
+
+DECLARE_FIELD( dPhaseViscosity,
+               "dPhaseViscosity",
+               array4dLayoutPhase_d,
+               0,
+               NOPLOT,
+               NO_WRITE,
+               "Derivative of phase viscosity with respect to pressure" );
+
+} // namespace twophasefluid
+
+} // namespace constitutive
+} // namespace geos
+
+#endif // GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUIDFIELDS_HPP_
diff --git a/src/coreComponents/constitutive/unitTests/FluidModelTest_impl.hpp b/src/coreComponents/constitutive/unitTests/FluidModelTest_impl.hpp
index 72cfec6501c..ce731e6b775 100644
--- a/src/coreComponents/constitutive/unitTests/FluidModelTest_impl.hpp
+++ b/src/coreComponents/constitutive/unitTests/FluidModelTest_impl.hpp
@@ -35,7 +35,7 @@ template< typename FLUID_TYPE, integer NUM_COMP, integer NUM_PHASE >
 FluidModelTest< FLUID_TYPE, NUM_COMP, NUM_PHASE >::FluidModelTest():
   m_parent( "parent", m_node )
 {
-  createFunctionManager();
+  // createFunctionManager();
 }
 
 template< typename FLUID_TYPE, integer NUM_COMP, integer NUM_PHASE >
diff --git a/src/coreComponents/constitutive/unitTests/testCO2SpycherPruessModels.cpp.uncrustify b/src/coreComponents/constitutive/unitTests/testCO2SpycherPruessModels.cpp.uncrustify
new file mode 100644
index 00000000000..e69de29bb2d
diff --git a/src/coreComponents/constitutive/unitTests/testTwoPhaseFluid.cpp b/src/coreComponents/constitutive/unitTests/testTwoPhaseFluid.cpp
new file mode 100644
index 00000000000..207668e29cb
--- /dev/null
+++ b/src/coreComponents/constitutive/unitTests/testTwoPhaseFluid.cpp
@@ -0,0 +1,283 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 TotalEnergies
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+#include "constitutive/fluid/twophasefluid/TwoPhaseFluid.hpp"
+#include "constitutive/fluid/twophasefluid/TwoPhaseFluidFields.hpp"
+
+// Only for fill
+#include "unitTests/constitutiveTests/MultiFluidTest.hpp"
+
+// Only for initializeTable
+#include "unitTests/constitutiveTests/constitutiveTestHelpers.hpp"
+
+
+using namespace geos;
+using namespace geos::testing;
+using namespace geos::constitutive;
+using namespace geos::dataRepository;   /// Only for group definition
+
+
+static constexpr char const * tableContentPhase0 = "# Pg(Pa) Dens(kg/m3) Visc(Pa.s)\n"
+                                                   "0.22     0.00603  40203\n"
+                                                   "0.3      0.04224  31311\n"
+                                                   "0.5      0.15011  22423\n"
+                                                   "0.6      0.22423  15011\n"
+                                                   "0.8      0.31311  4224\n"
+                                                   "1.0      0.40203  603";
+
+static constexpr char const * tableContentPhase1 = "# Pg(Pa) Dens(kg/m3) Visc(Pa.s)\n"
+                                                   "1.22     0.00603  0.22\n"
+                                                   "1.3      0.04224  0.22\n"
+                                                   "1.5      0.15011  0.22\n"
+                                                   "1.6      0.22423  0.22\n"
+                                                   "1.8      0.31311  0.22\n"
+                                                   "2.0      0.40203  0.22";
+
+template< bool FROM_TABLE >
+class TwoPhaseFluidTest : public ConstitutiveTestBase< TwoPhaseFluid >
+{
+public:
+
+  TwoPhaseFluidTest()
+  {
+    if constexpr (!FROM_TABLE)
+    {
+      writeTableToFile( "phase0.txt", tableContentPhase0 );
+      writeTableToFile( "phase1.txt", tableContentPhase1 );
+    }
+
+    m_parent.resize( 1 );
+    string const fluidName = GEOS_FMT( "fluid{}", (FROM_TABLE ? "Tables" : "Files"));
+    m_model = makeTwoPhaseFluid( fluidName, m_parent );
+
+    m_parent.initialize();
+    m_parent.initializePostInitialConditions();
+  }
+
+  ~TwoPhaseFluidTest()
+  {
+    if constexpr (!FROM_TABLE)
+    {
+      removeFile( "phase0.txt" );
+      removeFile( "phase1.txt" );
+    }
+  }
+
+  constitutive::TwoPhaseFluid & getFluid() const { return *m_model; }
+
+  dataRepository::Group & getParent() { return m_parent; }
+
+
+  void testDerivatives( constitutive::TwoPhaseFluid & fluid,
+                        dataRepository::Group * parent,
+                        real64 const pressure,
+                        real64 const perturbParameter,
+                        real64 const relTol,
+                        real64 const absTol = std::numeric_limits< real64 >::max() )
+  {
+    auto const & phaseNames = fluid.getReference< string_array >( TwoPhaseFluid::viewKeyStruct::phaseNamesString() );
+
+    // create a clone of the fluid to run updates on
+    string const fluidCopyName = fluid.getName() + "Copy";
+    std::unique_ptr< constitutive::ConstitutiveBase > fluidCopyPtr = fluid.deliverClone( fluidCopyName, parent );
+    constitutive::TwoPhaseFluid & fluidCopy = dynamicCast< constitutive::TwoPhaseFluid & >( *fluidCopyPtr );
+    fluidCopy.initializePostSubGroups();
+
+    fluid.allocateConstitutiveData( fluid.getParent(), 1 );
+    fluidCopy.allocateConstitutiveData( fluid.getParent(), 1 );
+
+    // extract data views from both fluids
+    #define GET_FLUID_DATA( FLUID, TRAIT ) \
+      FLUID.getReference< TRAIT::type >( TRAIT::key() )[0][0]
+
+    constitutive::MultiFluidVarSlice< real64, 1, constitutive::multifluid::USD_PHASE - 2, constitutive::multifluid::USD_PHASE_DC - 2 > phaseVisc {
+      GET_FLUID_DATA( fluid, fields::twophasefluid::phaseViscosity ),
+      GET_FLUID_DATA( fluid, fields::twophasefluid::dPhaseViscosity )
+    };
+
+    constitutive::MultiFluidVarSlice< real64, 1, constitutive::multifluid::USD_PHASE - 2, constitutive::multifluid::USD_PHASE_DC - 2 > phaseDens {
+      GET_FLUID_DATA( fluid, fields::twophasefluid::phaseDensity ),
+      GET_FLUID_DATA( fluid, fields::twophasefluid::dPhaseDensity )
+    };
+
+    auto const & phaseDensCopy = GET_FLUID_DATA( fluidCopy, fields::twophasefluid::phaseDensity );
+    auto const & phaseViscCopy = GET_FLUID_DATA( fluidCopy, fields::twophasefluid::phaseViscosity );
+#undef GET_FLUID_DATA
+
+
+    // set the original fluid state to current
+    constitutive::constitutiveUpdatePassThru( fluid, [&] ( auto & castedFluid )
+    {
+      typename TYPEOFREF( castedFluid ) ::KernelWrapper fluidWrapper = castedFluid.createKernelWrapper();
+      fluidWrapper.update( 0, 0, pressure );
+    } );
+
+    // now perturb variables and update the copied fluid's state
+    constitutive::constitutiveUpdatePassThru( fluidCopy, [&] ( auto & castedFluid )
+    {
+      using Deriv = constitutive::multifluid::DerivativeOffset;
+
+      typename TYPEOFREF( castedFluid ) ::KernelWrapper fluidWrapper = castedFluid.createKernelWrapper();
+
+      // to be able to use the checkDerivative utility function, we have to invert the layout
+      auto dPhaseDens     = invertLayout( phaseDens.derivs.toSliceConst(), 2, 1 );
+      auto dPhaseVisc     = invertLayout( phaseVisc.derivs.toSliceConst(), 2, 1 );
+
+      // update pressure and check derivatives
+      real64 const dP = perturbParameter * (pressure + perturbParameter);
+      fluidWrapper.update( 0, 0, pressure + dP );
+
+      checkDerivative( phaseDensCopy.toSliceConst(), phaseDens.value.toSliceConst(), dPhaseDens[Deriv::dP].toSliceConst(),
+                       dP, relTol, absTol, "phaseDens", "Pressure", phaseNames );
+      checkDerivative( phaseViscCopy.toSliceConst(), phaseVisc.value.toSliceConst(), dPhaseVisc[Deriv::dP].toSliceConst(),
+                       dP, relTol, absTol, "phaseVisc", "Pressure", phaseNames );
+    } );
+  }   // void testDerivatives
+
+
+protected:
+  static void writeTableToFile( string const & fileName, char const * content )
+  {
+    std::ofstream os( fileName );
+    ASSERT_TRUE( os.is_open() );
+    os << content;
+    os.close();
+  }
+
+  static void removeFile( string const & fileName )
+  {
+    int const ret = std::remove( fileName.c_str() );
+    ASSERT_TRUE( ret == 0 );
+  }
+
+
+private:
+  static TwoPhaseFluid * makeTwoPhaseFluid( string const & name, Group & parent );
+
+};  // class TwoPhaseFluidTest
+
+
+template<>
+TwoPhaseFluid * TwoPhaseFluidTest< true >::makeTwoPhaseFluid( string const & name, Group & parent )
+{
+  // 1D table with linear interpolation
+  localIndex constexpr Naxis = 6;
+  localIndex constexpr NaxisSingle = 1;
+
+  array1d< real64_array > densityCoordPhase0( 1 );
+  fill< Naxis >( densityCoordPhase0[0], { 0.22, 0.3, 0.5, 0.6, 0.8, 1.0 } );
+  real64_array densityValuesPhase0;
+  fill< Naxis >( densityValuesPhase0, { 0.00603, 0.04224, 0.04224, 0.22423, 0.31311, 0.40203 } );
+
+  array1d< real64_array > densityCoordPhase1( 1 );
+  fill< Naxis >( densityCoordPhase1[0], { 1.22, 1.3, 1.5, 1.6, 1.8, 2.0 } );
+  real64_array densityValuesPhase1;
+  fill< Naxis >( densityValuesPhase1, { 0.00603, 0.04224, 0.04224, 0.22423, 0.31311, 0.40203 } );
+
+
+  array1d< real64_array > viscosityCoordPhase0( 1 );
+  fill< Naxis >( viscosityCoordPhase0[0], { 0.22, 0.3, 0.5, 0.6, 0.8, 1.0 } );
+  real64_array viscosityValuesPhase0;
+  fill< Naxis >( viscosityValuesPhase0, { 40203, 31311, 22423, 15011, 4224, 603 } );
+
+  array1d< real64_array > viscosityCoordPhase1( 1 );
+  fill< NaxisSingle >( viscosityCoordPhase1[0], { 0.22 } );
+  real64_array viscosityValuesPhase1;
+  fill< NaxisSingle >( viscosityValuesPhase1, { 45 } );
+
+  initializeTable( "densityTablePhase0", densityCoordPhase0, densityValuesPhase0 );
+  initializeTable( "densityTablePhase1", densityCoordPhase1, densityValuesPhase1 );
+  initializeTable( "viscosityTablePhase0", viscosityCoordPhase0, viscosityValuesPhase0 );
+  initializeTable( "viscosityTablePhase1", viscosityCoordPhase1, viscosityValuesPhase1 );
+
+
+  // 2) Set up the constitutive model
+  TwoPhaseFluid & fluid = parent.registerGroup< TwoPhaseFluid >( name );
+
+  string_array & phaseNames = fluid.getReference< string_array >( TwoPhaseFluid::viewKeyStruct::phaseNamesString() );
+  phaseNames.emplace_back( "oil" );
+  phaseNames.emplace_back( "water" );
+
+  string_array & densityTableNames = fluid.getReference< string_array >( TwoPhaseFluid::viewKeyStruct::densityTableNamesString() );
+  densityTableNames.emplace_back( "densityTablePhase0" );
+  densityTableNames.emplace_back( "densityTablePhase1" );
+
+  string_array & viscosityTableNames = fluid.getReference< string_array >( TwoPhaseFluid::viewKeyStruct::viscosityTableNamesString() );
+  viscosityTableNames.emplace_back( "viscosityTablePhase0" );
+  viscosityTableNames.emplace_back( "viscosityTablePhase1" );
+
+  fluid.postInputInitializationRecursive();
+  return &fluid;
+}
+
+
+template<>
+TwoPhaseFluid * TwoPhaseFluidTest< false >::makeTwoPhaseFluid( string const & name, Group & parent )
+{
+  TwoPhaseFluid & fluid = parent.registerGroup< TwoPhaseFluid >( name );
+
+  path_array & tableNames = fluid.getReference< path_array >( TwoPhaseFluid::viewKeyStruct::tableFilesString() );
+  fill< 2 >( tableNames, {"phase0.txt", "phase1.txt"} );
+
+  fluid.postInputInitializationRecursive();
+  return &fluid;
+}
+
+
+
+using TwoPhaseFluidTestFromFiles = TwoPhaseFluidTest< false >;
+using TwoPhaseFluidTestFromTables = TwoPhaseFluidTest< true >;
+
+
+TEST_F( TwoPhaseFluidTestFromTables, testNumericalDerivative_initFromTables )
+{
+  auto & fluid = getFluid();
+  real64 const eps = std::sqrt( std::numeric_limits< real64 >::epsilon());
+  real64 constexpr relTol = 1.0e-8;
+  real64 constexpr absTol = 1.0e-8;
+
+  for( real64 const pressure : { 0.55, 1.0, 10.0 } )
+  {
+    testDerivatives( fluid, &getParent(), pressure, eps, relTol, absTol );
+  }
+}
+
+
+TEST_F( TwoPhaseFluidTestFromFiles, testNumericalDerivative_initFromFiles )
+{
+  auto & fluid = getFluid();
+  real64 const eps = std::sqrt( std::numeric_limits< real64 >::epsilon());
+  real64 constexpr relTol = 1.0e-8;
+  real64 constexpr absTol = 1.0e-8;
+
+  for( real64 const pressure : { 0.55, 1.0, 10.0 } )
+  {
+    testDerivatives( fluid, &getParent(), pressure, eps, relTol, absTol );
+  }
+}
+
+
+int main( int argc, char * * argv )
+{
+  ::testing::InitGoogleTest( &argc, argv );
+
+  conduit::Node conduitNode;
+  dataRepository::Group rootNode( "root", conduitNode );
+  FunctionManager functionManager( "FunctionManager", &rootNode );
+
+  int const result = RUN_ALL_TESTS();
+
+  return result;
+}
diff --git a/src/coreComponents/finiteVolume/CellElementStencilTPFA.hpp b/src/coreComponents/finiteVolume/CellElementStencilTPFA.hpp
index 88fa3bb2b27..5c468d293cf 100644
--- a/src/coreComponents/finiteVolume/CellElementStencilTPFA.hpp
+++ b/src/coreComponents/finiteVolume/CellElementStencilTPFA.hpp
@@ -70,6 +70,20 @@ class CellElementStencilTPFAWrapper : public StencilWrapperBase< TwoPointStencil
                        CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
                        real64 ( &weight )[1][2],
                        real64 ( &dWeight_dVar )[1][2] ) const;
+/**
+ * @brief Compute half weights and derivatives w.r.t to one variable.
+ * @param[in] iconn connection index
+ * @param[in] coefficient view accessor to the coefficient used to compute the weights
+ * @param[in] dCoeff_dVar view accessor to the derivative of the coefficient w.r.t to the variable
+ * @param[out] weight view weights
+ * @param[out] dWeight_dVar derivative of the weights w.r.t to the variable
+ */
+  GEOS_HOST_DEVICE
+  void computeHalfWeights( localIndex const iconn,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                           real64 ( &weight )[1][2],
+                           real64 ( &dWeight_dVar )[1][2] ) const;
 
   /**
    * @brief Compute weights and derivatives w.r.t to one variable without coefficient
@@ -293,6 +307,92 @@ CellElementStencilTPFAWrapper::
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+CellElementStencilTPFAWrapper::
+  computeHalfWeights( localIndex const iconn,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                      real64 (& weight)[1][2],
+                      real64 (& dWeight_dVar )[1][2] ) const
+{
+  real64 halfWeight[2];
+  real64 dHalfWeight_dVar[2];
+
+  // real64 const tolerance = 1e-30 * lengthTolerance; // TODO: choice of constant based on physics?
+
+  for( localIndex i = 0; i < 2; ++i )
+  {
+    localIndex const er  = m_elementRegionIndices[iconn][i];
+    localIndex const esr = m_elementSubRegionIndices[iconn][i];
+    localIndex const ei  = m_elementIndices[iconn][i];
+
+    halfWeight[i] = m_weights[iconn][i];
+    dHalfWeight_dVar[i] = m_weights[iconn][i];
+
+    // Proper computation
+    real64 faceNormal[3];
+    LvArray::tensorOps::copy< 3 >( faceNormal, m_faceNormal[iconn] );
+    if( LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn][i], faceNormal ) < 0.0 )
+    {
+      LvArray::tensorOps::scale< 3 >( faceNormal, -1 );
+    }
+
+    real64 faceConormal[3];
+    real64 dFaceConormal_dVar[3];
+    LvArray::tensorOps::hadamardProduct< 3 >( faceConormal, coefficient[er][esr][ei][0], faceNormal );
+    LvArray::tensorOps::hadamardProduct< 3 >( dFaceConormal_dVar, dCoeff_dVar[er][esr][ei][0], faceNormal );
+    halfWeight[i] *= LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn][i], faceConormal );
+    dHalfWeight_dVar[i] *= LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn][i], dFaceConormal_dVar );
+
+    // correct negative weight issue arising from non-K-orthogonal grids
+    // if( halfWeight[i] < 0.0 )
+    // {
+    //   LvArray::tensorOps::hadamardProduct< 3 >( faceConormal,
+    //                                             coefficient[er][esr][ei][0],
+    //                                             m_cellToFaceVec[iconn][i] );
+    //   LvArray::tensorOps::hadamardProduct< 3 >( dFaceConormal_dVar,
+    //                                             dCoeff_dVar[er][esr][ei][0],
+    //                                             m_cellToFaceVec[iconn][i] );
+    //   halfWeight[i] = m_weights[iconn][i];
+    //   dHalfWeight_dVar[i] = m_weights[iconn][i];
+    //   halfWeight[i] *= LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn][i], faceConormal );
+    //   dHalfWeight_dVar[i] *= LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn][i], dFaceConormal_dVar );
+    // }
+  }
+
+  // // Do harmonic and arithmetic averaging
+  // real64 const product = halfWeight[0]*halfWeight[1];
+  // real64 const sum = halfWeight[0]+halfWeight[1];
+
+  // real64 const harmonicWeight   = sum > 0 ? product / sum : 0.0;
+  // real64 const arithmeticWeight = sum / 2;
+
+  // real64 dHarmonicWeight_dVar[2];
+  // real64 dArithmeticWeight_dVar[2];
+
+  // dHarmonicWeight_dVar[0] = sum > 0 ? (dHalfWeight_dVar[0]*sum*halfWeight[1] - dHalfWeight_dVar[0]*halfWeight[0]*halfWeight[1]) / (
+  // sum*sum ) : 0.0;
+  // dHarmonicWeight_dVar[1] = sum > 0 ? (dHalfWeight_dVar[1]*sum*halfWeight[0] - dHalfWeight_dVar[1]*halfWeight[1]*halfWeight[0]) / (
+  // sum*sum ) : 0.0;
+
+  // dArithmeticWeight_dVar[0] = dHalfWeight_dVar[0] / 2;
+  // dArithmeticWeight_dVar[1] = dHalfWeight_dVar[1] / 2;
+
+  // real64 const meanPermCoeff = 1.0; //TODO make it a member if it is really necessary
+
+  // real64 const value = meanPermCoeff * harmonicWeight + (1 - meanPermCoeff) * arithmeticWeight;
+  for( localIndex ke = 0; ke < 2; ++ke )
+  {
+    // weight[0][ke] = m_transMultiplier[iconn] * value * (ke == 0 ? 1 : -1);
+    weight[0][ke] = m_transMultiplier[iconn] * halfWeight[ke] * (ke == 0 ? 1 : -1);
+
+    // real64 const dValue_dVar = meanPermCoeff * dHarmonicWeight_dVar[ke] + (1 - meanPermCoeff) * dArithmeticWeight_dVar[ke];
+    // dWeight_dVar[0][ke] = m_transMultiplier[iconn] * dValue_dVar;
+    dWeight_dVar[0][ke] = m_transMultiplier[iconn] * dHalfWeight_dVar[ke];
+  }
+}
+
 GEOS_HOST_DEVICE
 inline void
 CellElementStencilTPFAWrapper::
diff --git a/src/coreComponents/finiteVolume/EmbeddedSurfaceToCellStencil.hpp b/src/coreComponents/finiteVolume/EmbeddedSurfaceToCellStencil.hpp
index 7f9c1562366..4a191ca7614 100644
--- a/src/coreComponents/finiteVolume/EmbeddedSurfaceToCellStencil.hpp
+++ b/src/coreComponents/finiteVolume/EmbeddedSurfaceToCellStencil.hpp
@@ -98,6 +98,22 @@ class EmbeddedSurfaceToCellStencilWrapper : public StencilWrapperBase< TwoPointS
                        real64 ( &weight )[1][2],
                        real64 ( &dWeight_dVar )[1][2] ) const;
 
+  /**
+   * @brief Compute half weigths and derivatives w.r.t to one variable.
+   * @param[in] iconn connection index
+   * @param[in] coefficient view accessor to the coefficient used to compute the weights
+   * @param[in] dCoeff_dVar view accessor to the derivative of the coefficient w.r.t to the variable
+   * @param[out] weight view weights
+   * @param[out] dWeight_dVar derivative of the weigths w.r.t to the variable
+   */
+
+  GEOS_HOST_DEVICE
+  void computeHalfWeights( localIndex const iconn,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                           real64 ( &weight )[1][2],
+                           real64 ( &dWeight_dVar )[1][2] ) const;
+
   /**
    * @brief Compute weigths and derivatives w.r.t to one variable without coefficient
    * Used in ReactiveCompositionalMultiphaseOBL solver for thermal transmissibility computation:
@@ -243,6 +259,42 @@ EmbeddedSurfaceToCellStencilWrapper::
   dWeight_dVar[0][1] = ( t0 * dt1 * sumOfTrans - dt1 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
 }
 
+GEOS_HOST_DEVICE
+inline void
+EmbeddedSurfaceToCellStencilWrapper::
+  computeHalfWeights( localIndex iconn,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                      real64 ( & weight )[1][2],
+                      real64 ( & dWeight_dVar )[1][2] ) const
+{
+  localIndex const er0  =  m_elementRegionIndices[iconn][0];
+  localIndex const esr0 =  m_elementSubRegionIndices[iconn][0];
+  localIndex const ei0  =  m_elementIndices[iconn][0];
+
+  localIndex const er1  =  m_elementRegionIndices[iconn][1];
+  localIndex const esr1 =  m_elementSubRegionIndices[iconn][1];
+  localIndex const ei1  =  m_elementIndices[iconn][1];
+
+  // Will change when implementing collocation points. Will use fracture normal to project the permeability
+  real64 const t0 = m_weights[iconn][0] * LvArray::tensorOps::l2Norm< 3 >( coefficient[er0][esr0][ei0][0] );
+  // We consider the 3rd component of the permeability which is the normal one.
+  real64 const t1 = m_weights[iconn][1] * coefficient[er1][esr1][ei1][0][2];
+
+  real64 const sumOfTrans = t0+t1;
+  real64 const value = t0*t1/sumOfTrans;
+
+  weight[0][0] = value;
+  weight[0][1] = -value;
+
+  // We consider the 3rd component of the permeability which is the normal one.
+  real64 const dt0 = m_weights[iconn][0] * dCoeff_dVar[er0][esr0][ei0][0][0];
+  real64 const dt1 = m_weights[iconn][1] * dCoeff_dVar[er1][esr1][ei1][0][2];
+
+  dWeight_dVar[0][0] = ( dt0 * t1 * sumOfTrans - dt0 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+  dWeight_dVar[0][1] = ( t0 * dt1 * sumOfTrans - dt1 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+}
+
 GEOS_HOST_DEVICE
 inline void
 EmbeddedSurfaceToCellStencilWrapper::
diff --git a/src/coreComponents/finiteVolume/FaceElementToCellStencil.hpp b/src/coreComponents/finiteVolume/FaceElementToCellStencil.hpp
index 6920e52b3bf..e86e6724bed 100644
--- a/src/coreComponents/finiteVolume/FaceElementToCellStencil.hpp
+++ b/src/coreComponents/finiteVolume/FaceElementToCellStencil.hpp
@@ -106,6 +106,21 @@ class FaceElementToCellStencilWrapper : public StencilWrapperBase< TwoPointStenc
                        real64 ( &weight )[1][2],
                        real64 ( &dWeight_dVar )[1][2] ) const;
 
+/**
+ * @brief Compute half weigths and derivatives w.r.t to one variable.
+ * @param[in] iconn connection index
+ * @param[in] coefficient view accessor to the coefficient used to compute the weights
+ * @param[in] dCoeff_dVar view accessor to the derivative of the coefficient w.r.t to the variable
+ * @param[out] weight view weights
+ * @param[out] dWeight_dVar derivative of the weigths w.r.t to the variable
+ */
+  GEOS_HOST_DEVICE
+  void computeHalfWeights( localIndex iconn,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                           real64 ( &weight )[1][2],
+                           real64 ( &dWeight_dVar )[1][2] ) const;
+
   /**
    * @brief Compute weigths and derivatives w.r.t to one variable without coefficient
    * Used in ReactiveCompositionalMultiphaseOBL solver for thermal transmissibility computation:
@@ -297,6 +312,44 @@ inline void FaceElementToCellStencilWrapper::
   dWeight_dVar[0][1] = m_transMultiplier[iconn] * ( t0 * dt1 * sumOfTrans - dt1 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
 }
 
+GEOS_HOST_DEVICE
+inline void FaceElementToCellStencilWrapper::
+  computeHalfWeights( localIndex const iconn,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                      real64 ( & weight )[1][2],
+                      real64 ( & dWeight_dVar )[1][2] ) const
+{
+  localIndex const er0  =  m_elementRegionIndices[iconn][0];
+  localIndex const esr0 =  m_elementSubRegionIndices[iconn][0];
+  localIndex const ei0  =  m_elementIndices[iconn][0];
+
+  localIndex const er1  =  m_elementRegionIndices[iconn][1];
+  localIndex const esr1 =  m_elementSubRegionIndices[iconn][1];
+  localIndex const ei1  =  m_elementIndices[iconn][1];
+
+  real64 faceConormal[3];
+
+  // Will change when implementing collocation points.
+  LvArray::tensorOps::hadamardProduct< 3 >( faceConormal, coefficient[er0][esr0][ei0][0], m_faceNormal[iconn] );
+  real64 const t0 = m_weights[iconn][0] * LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn], faceConormal );
+  // We consider the 3rd component of the permeability which is the normal one.
+  real64 const t1 = m_weights[iconn][1] * coefficient[er1][esr1][ei1][0][2];
+
+  real64 const sumOfTrans = t0+t1;
+  real64 const value = m_transMultiplier[iconn]*t0*t1/sumOfTrans;
+
+  weight[0][0] = value;
+  weight[0][1] = -value;
+
+  // We consider the 3rd component of the permeability which is the normal one.
+  real64 const dt0 = m_weights[iconn][0] * dCoeff_dVar[er0][esr0][ei0][0][0];
+  real64 const dt1 = m_weights[iconn][1] * dCoeff_dVar[er1][esr1][ei1][0][2];
+
+  dWeight_dVar[0][0] = ( dt0 * t1 * sumOfTrans - dt0 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+  dWeight_dVar[0][1] = ( t0 * dt1 * sumOfTrans - dt1 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+}
+
 GEOS_HOST_DEVICE
 inline void
 FaceElementToCellStencilWrapper
diff --git a/src/coreComponents/finiteVolume/SurfaceElementStencil.hpp b/src/coreComponents/finiteVolume/SurfaceElementStencil.hpp
index 5de67fe2f11..4c982dbef4a 100644
--- a/src/coreComponents/finiteVolume/SurfaceElementStencil.hpp
+++ b/src/coreComponents/finiteVolume/SurfaceElementStencil.hpp
@@ -110,6 +110,21 @@ class SurfaceElementStencilWrapper : public StencilWrapperBase< SurfaceElementSt
                        real64 ( &weight )[maxNumConnections][2],
                        real64 ( &dWeight_dVar )[maxNumConnections][2] ) const;
 
+  /**
+   * @brief Compute weights and derivatives w.r.t to one variable.
+   * @param[in] iconn connection index
+   * @param[in] coefficient view accessor to the coefficient used to compute the weights
+   * @param[in] dCoeff_dVar view accessor to the derivative of the coefficient w.r.t to the variable
+   * @param[out] weight view weights
+   * @param[out] dWeight_dVar derivative of the weights w.r.t to the variable
+   */
+  GEOS_HOST_DEVICE
+  void computeHalfWeights( localIndex iconn,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                           real64 ( &weight )[maxNumConnections][2],
+                           real64 ( &dWeight_dVar )[maxNumConnections][2] ) const;
+
   /**
    * @brief Compute weights and derivatives w.r.t to one variable without coefficient
    * Used in ReactiveCompositionalMultiphaseOBL solver for thermal transmissibility computation:
@@ -364,6 +379,70 @@ SurfaceElementStencilWrapper::
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+SurfaceElementStencilWrapper::
+  computeHalfWeights( localIndex iconn,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                      real64 ( & weight )[maxNumConnections][2],
+                      real64 ( & dWeight_dVar )[maxNumConnections][2] ) const
+{
+
+  real64 sumOfTrans = 0.0;
+  for( localIndex k=0; k<numPointsInFlux( iconn ); ++k )
+  {
+    localIndex const er  =  m_elementRegionIndices[iconn][k];
+    localIndex const esr =  m_elementSubRegionIndices[iconn][k];
+    localIndex const ei  =  m_elementIndices[iconn][k];
+
+    sumOfTrans += coefficient[er][esr][ei][0][0] * m_weights[iconn][k];
+  }
+
+  localIndex k[2];
+  localIndex connectionIndex = 0;
+  for( k[0]=0; k[0]<numPointsInFlux( iconn ); ++k[0] )
+  {
+    for( k[1]=k[0]+1; k[1]<numPointsInFlux( iconn ); ++k[1] )
+    {
+      localIndex const er0  =  m_elementRegionIndices[iconn][k[0]];
+      localIndex const esr0 =  m_elementSubRegionIndices[iconn][k[0]];
+      localIndex const ei0  =  m_elementIndices[iconn][k[0]];
+
+      localIndex const er1  =  m_elementRegionIndices[iconn][k[1]];
+      localIndex const esr1 =  m_elementSubRegionIndices[iconn][k[1]];
+      localIndex const ei1  =  m_elementIndices[iconn][k[1]];
+
+      real64 const t0 = m_weights[iconn][0] * coefficient[er0][esr0][ei0][0][0]; // this is a bit insane to access perm
+      real64 const t1 = m_weights[iconn][1] * coefficient[er1][esr1][ei1][0][0];
+
+      real64 const harmonicWeight   = t0*t1 / sumOfTrans;
+      real64 const arithmeticWeight = 0.25 * (t0+t1);
+
+      real64 const value = m_meanPermCoefficient * harmonicWeight + (1 - m_meanPermCoefficient) * arithmeticWeight;
+
+      weight[connectionIndex][0] = value;
+      weight[connectionIndex][1] = -value;
+
+      real64 const dt0 = m_weights[iconn][0] * dCoeff_dVar[er0][esr0][ei0][0][0];
+      real64 const dt1 = m_weights[iconn][1] * dCoeff_dVar[er1][esr1][ei1][0][0];
+
+      real64 dHarmonic[2];
+      dHarmonic[0] = ( dt0 * t1 * sumOfTrans - dt0 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+      dHarmonic[1] = ( t0 * dt1 * sumOfTrans - dt1 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+
+      real64 dArithmetic[2];
+      dArithmetic[0] = 0.25 * dt0;
+      dArithmetic[1] = 0.25 * dt1;
+
+      dWeight_dVar[connectionIndex][0] = m_meanPermCoefficient * dHarmonic[0] + (1 - m_meanPermCoefficient) * dArithmetic[0];
+      dWeight_dVar[connectionIndex][1] = -( m_meanPermCoefficient * dHarmonic[1] + (1 - m_meanPermCoefficient) * dArithmetic[1] );
+
+      connectionIndex++;
+    }
+  }
+}
+
 GEOS_HOST_DEVICE
 inline void
 SurfaceElementStencilWrapper::
diff --git a/src/coreComponents/integrationTests/fluidFlowTests/CMakeLists.txt b/src/coreComponents/integrationTests/fluidFlowTests/CMakeLists.txt
index 951cac7c502..9a89d938e2e 100644
--- a/src/coreComponents/integrationTests/fluidFlowTests/CMakeLists.txt
+++ b/src/coreComponents/integrationTests/fluidFlowTests/CMakeLists.txt
@@ -4,6 +4,7 @@ set( gtest_geosx_tests
      testThermalSinglePhaseFlow.cpp
      testTransmissibility.cpp
      testImmiscibleMultiphaseFlow.cpp
+     testImmiscibleInterfaceConditions.cpp
      testSinglePhaseMFDPolyhedral.cpp
      testSinglePhaseReactiveTransport.cpp )
 
diff --git a/src/coreComponents/integrationTests/fluidFlowTests/testImmiscibleInterfaceConditions.cpp b/src/coreComponents/integrationTests/fluidFlowTests/testImmiscibleInterfaceConditions.cpp
new file mode 100644
index 00000000000..e3fd4cdb38e
--- /dev/null
+++ b/src/coreComponents/integrationTests/fluidFlowTests/testImmiscibleInterfaceConditions.cpp
@@ -0,0 +1,686 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 TotalEnergies
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+#define phase0MinSat1 0.0
+#define phase1MinSat1 0.0
+#define phase0MinSat2 0.0
+#define phase1MinSat2 0.0
+
+
+#include <chrono>
+#include <iostream>
+
+#include "mainInterface/initialization.hpp"
+#include "mainInterface/GeosxState.hpp"
+#include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluid.hpp"
+#include "physicsSolvers/PhysicsSolverManager.hpp"
+#include "physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.hpp"
+#include "integrationTests/fluidFlowTests/testCompFlowUtils.hpp"
+#include "constitutive/unitTests/FluidModelTest.hpp"
+#include "constitutive/unitTests/FluidModelTest_impl.hpp"
+#include "common/initializeEnvironment.hpp"
+#include "constitutive/relativePermeability/unitTests/constitutiveTestHelpers.hpp"
+#include "functions/FunctionManager.hpp"
+#include "constitutive/capillaryPressure/CapillaryPressureFields.hpp"
+
+#include <conduit.hpp>
+
+
+
+using namespace geos;
+using namespace geos::dataRepository;
+using namespace geos::constitutive;
+using namespace geos::testing;
+
+CommandLineOptions g_commandLineOptions;
+
+TwoPhaseImmiscibleFluid * makeTwoPhaseImmiscibleFluid( TwoPhaseImmiscibleFluid & fluid )
+{
+
+  FunctionManager & functionManager = FunctionManager::getInstance();
+
+  // 1D table with linear interpolation
+  localIndex constexpr Naxis = 6;
+  localIndex constexpr NaxisSingle = 1;
+
+  real64_array densityCoordPhase0;
+  // fill( densityCoordPhase0, Feed< Naxis >{ 0.22, 0.3, 0.5, 0.6, 0.8, 1.0 } );
+  for( auto v : {0.0} )
+    densityCoordPhase0.emplace_back( v );
+  real64_array densityValuesPhase0;
+  // fill( densityValuesPhase0, Feed< Naxis >{ 0.00603, 0.04224, 0.04224, 0.22423, 0.31311, 0.40203 } );
+  for( auto v : {1000.0} )
+    densityValuesPhase0.emplace_back( v );
+
+  real64_array densityCoordPhase1;
+  // fill( densityCoordPhase1, Feed< Naxis >{ 1.22, 1.3, 1.5, 1.6, 1.8, 2.0 } );
+  for( auto v : {0.0} )
+    densityCoordPhase1.emplace_back( v );
+  real64_array densityValuesPhase1;
+  // fill( densityValuesPhase1, Feed< Naxis >{ 0.00603, 0.04224, 0.04224, 0.22423, 0.31311, 0.40203 } );
+  for( auto v : {100.0} )
+    densityValuesPhase1.emplace_back( v );
+
+  real64_array viscosityCoordPhase0;
+  // fill( viscosityCoordPhase0, Feed< Naxis >{ 0.22, 0.3, 0.5, 0.6, 0.8, 1.0 } );
+  for( auto v : {0.0} )
+    viscosityCoordPhase0.emplace_back( v );
+  real64_array viscosityValuesPhase0;
+  // fill( viscosityValuesPhase0, Feed< Naxis >{ 40203, 31311, 22423, 15011, 4224, 603 } );
+  for( auto v : {0.001} )
+    viscosityValuesPhase0.emplace_back( v );
+
+  real64_array viscosityCoordPhase1;
+  // fill( viscosityCoordPhase1, Feed< NaxisSingle >{ 0.22 } );
+  for( auto v : {0.0} )
+    viscosityCoordPhase1.emplace_back( v );
+
+  real64_array viscosityValuesPhase1;
+  // fill( viscosityValuesPhase1, Feed< NaxisSingle >{ 45 } );
+  for( auto v : {0.001} )
+    viscosityValuesPhase1.emplace_back( v );
+
+  TableFunction & table_density0 = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "densityTablePhase0" ) );
+  array1d< real64_array > coords_density0;
+  coords_density0.emplace_back( densityCoordPhase0 );
+  table_density0.setTableCoordinates( coords_density0, { units::Dimensionless } );
+  table_density0.setTableValues( densityValuesPhase0, units::Dimensionless );
+  table_density0.reInitializeFunction();
+
+  table_density0.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  TableFunction & table_density1 = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "densityTablePhase1" ) );
+  array1d< real64_array > coords_density1;
+  coords_density1.emplace_back( densityCoordPhase1 );
+  table_density1.setTableCoordinates( coords_density1, { units::Dimensionless } );
+  table_density1.setTableValues( densityValuesPhase1, units::Dimensionless );
+  table_density1.reInitializeFunction();
+
+  table_density1.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  TableFunction & table_viscosity0 = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "viscosityTablePhase0" ) );
+  array1d< real64_array > coords_viscosity0;
+  coords_viscosity0.emplace_back( viscosityCoordPhase0 );
+  table_viscosity0.setTableCoordinates( coords_viscosity0, { units::Dimensionless } );
+  table_viscosity0.setTableValues( viscosityValuesPhase0, units::Dimensionless );
+  table_viscosity0.reInitializeFunction();
+
+  table_viscosity0.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  TableFunction & table_viscosity1 = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "viscosityTablePhase1" ) );
+  array1d< real64_array > coords_viscosity1;
+  coords_viscosity1.emplace_back( viscosityCoordPhase1 );
+  table_viscosity1.setTableCoordinates( coords_viscosity1, { units::Dimensionless } );
+  table_viscosity1.setTableValues( viscosityValuesPhase1, units::Dimensionless );
+  table_viscosity1.reInitializeFunction();
+
+  table_viscosity1.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+
+  // createTable( "densityTablePhase0", densityCoordPhase0, densityValuesPhase0 );
+  // createTable( "densityTablePhase1", densityCoordPhase1, densityValuesPhase1 );
+  // createTable( "viscosityTablePhase0", viscosityCoordPhase0, viscosityValuesPhase0 );
+  // createTable( "viscosityTablePhase1", viscosityCoordPhase1, viscosityValuesPhase1 );
+
+  // 2) Set up the constitutive model
+
+  string_array & phaseNames = fluid.getReference< string_array >( TwoPhaseImmiscibleFluid::viewKeyStruct::phaseNamesString() );
+  phaseNames.emplace_back( "water" );
+  phaseNames.emplace_back( "gas" );
+
+  string_array & densityTableNames = fluid.getReference< string_array >( TwoPhaseImmiscibleFluid::viewKeyStruct::densityTableNamesString() );
+  densityTableNames.emplace_back( "densityTablePhase0" );
+  densityTableNames.emplace_back( "densityTablePhase1" );
+
+  string_array & viscosityTableNames = fluid.getReference< string_array >( TwoPhaseImmiscibleFluid::viewKeyStruct::viscosityTableNamesString() );
+  viscosityTableNames.emplace_back( "viscosityTablePhase0" );
+  viscosityTableNames.emplace_back( "viscosityTablePhase1" );
+
+  fluid.postInputInitializationRecursive();
+  fluid.initialize(); // to test all the checks
+
+  return &fluid;
+}
+
+CapillaryPressureBase & makeJFunctionCapPressureTwoPhase( string const & name, Group & parent )
+{
+  FunctionManager & functionManager = FunctionManager::getInstance();
+
+  // 1) First, define the tables
+
+  // // 1D table, various interpolation methods
+  // localIndex const Naxis = 12;
+
+  // // Setup table
+  // array1d< real64_array > coordinates;
+  // coordinates.resize( 1 );
+  // coordinates[0].resize( Naxis );
+
+  // coordinates[0][0] = 0.0;
+  // coordinates[0][1] = 0.05;
+  // coordinates[0][2] = 0.15;
+  // coordinates[0][3] = 0.25;
+  // coordinates[0][4] = 0.35;
+  // coordinates[0][5] = 0.45;
+  // coordinates[0][6] = 0.55;
+  // coordinates[0][7] = 0.65;
+  // coordinates[0][8] = 0.75;
+  // coordinates[0][9] = 0.85;
+  // coordinates[0][10] = 0.95;
+  // coordinates[0][11] = 1.0;
+
+  // real64_array values( Naxis );
+  // values[0] = 4.331729359;
+  // values[1] = 3.523266264;
+  // values[2] = 2.677103439;
+  // values[3] = 2.356150157;
+  // values[4] = 2.166062360;
+  // values[5] = 2.034158727;
+  // values[6] = 1.934627222;
+  // values[7] = 1.855494313;
+  // values[8] = 1.790286970;
+  // values[9] = 1.735134860;
+  // values[10] = 1.687551617;
+  // values[11] = 1.666049754;
+
+
+  localIndex const Naxis = 2;
+
+  // Setup table
+  array1d< real64_array > coordinates;
+  coordinates.resize( 1 );
+  coordinates[0].resize( Naxis );
+
+  coordinates[0][0] = 0.0;
+  coordinates[0][1] = 1.0;
+
+  real64_array values( Naxis );
+  values[0] = 4.331729359;
+  values[1] = 1.666049754;
+
+
+  TableFunction & table_w = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "water_jFunction" ) );
+  table_w.setTableCoordinates( coordinates, { units::Dimensionless } );
+  table_w.setTableValues( values, units::Dimensionless );
+  table_w.reInitializeFunction();
+
+  table_w.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  // 2) Then set up the constitutive model
+
+  JFunctionCapillaryPressure & capPressure = parent.registerGroup< JFunctionCapillaryPressure >( name );
+
+  string_array & phaseNames = capPressure.getReference< string_array >( CapillaryPressureBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  auto & waterTableName = capPressure.getReference< string >( JFunctionCapillaryPressure::viewKeyStruct::wettingNonWettingJFuncTableNameString() );
+  waterTableName = "water_jFunction";
+
+  auto & surfaceTension = capPressure.getReference< real64 >( JFunctionCapillaryPressure::viewKeyStruct::wettingNonWettingSurfaceTensionString() );
+  //surfaceTension = 23.86955676433857e-3;
+  surfaceTension = 0.02;
+
+  auto & permeabilityDirection =
+    capPressure.getReference< JFunctionCapillaryPressure::PermeabilityDirection >( JFunctionCapillaryPressure::viewKeyStruct::permeabilityDirectionString() );
+  permeabilityDirection = JFunctionCapillaryPressure::PermeabilityDirection::XY;
+
+  capPressure.postInputInitializationRecursive();
+  capPressure.initialize(); // to test all the checks
+
+  return capPressure;
+}
+
+CapillaryPressureBase & makeTableCapPressureTwoPhase1( string const & name, Group & parent )
+{
+  FunctionManager & functionManager = FunctionManager::getInstance();
+
+  // 1) First, define the tables
+
+  // 1D table, various interpolation methods
+  localIndex Naxis = 12;
+
+  // Setup table
+  array1d< real64_array > coordinates;
+  coordinates.resize( 1 );
+  coordinates[0].resize( Naxis );
+  coordinates[0][0] = 0.0;
+  coordinates[0][1] = 0.05;
+  coordinates[0][2] = 0.15;
+  coordinates[0][3] = 0.25;
+  coordinates[0][4] = 0.35;
+  coordinates[0][5] = 0.45;
+  coordinates[0][6] = 0.55;
+  coordinates[0][7] = 0.65;
+  coordinates[0][8] = 0.75;
+  coordinates[0][9] = 0.85;
+  coordinates[0][10] = 0.95;
+  coordinates[0][11] = 1.0;
+
+  real64_array values( Naxis );
+  values[0] = 130000.0;
+  values[1] = 90572.79;
+  values[2] = 49307.11;
+  values[3] = 33654.85;
+  values[4] = 24384.64;
+  values[5] = 17951.96;
+  values[6] = 13098;
+  values[7] = 9238.84;
+  values[8] = 6058.81;
+  values[9] = 3369.14;
+  values[10] = 1048.6;
+  values[11] = 0.0;
+
+  // localIndex const Naxis = 2;
+
+  // // Setup table
+  // array1d< real64_array > coordinates;
+  // coordinates.resize( 1 );
+  // coordinates[0].resize( Naxis );
+
+  // coordinates[0][0] = 0.0;
+  // coordinates[0][1] = 1.0;
+
+  // real64_array values( Naxis );
+  // values[0] = 129999.999994362;
+  // values[1] = 50000.0000139914;
+
+
+  TableFunction & table_w = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "water_pc" ) );
+  table_w.setTableCoordinates( coordinates, { units::Dimensionless } );
+  table_w.setTableValues( values, units::Pressure );
+  table_w.reInitializeFunction();
+
+  table_w.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  // 2) Then set up the constitutive model
+
+  TableCapillaryPressure & capPressure = parent.registerGroup< TableCapillaryPressure >( name );
+
+  string_array & phaseNames = capPressure.getReference< string_array >( CapillaryPressureBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  auto & waterTableName = capPressure.getReference< string >( TableCapillaryPressure::viewKeyStruct::wettingNonWettingCapPresTableNameString() );
+  waterTableName = "water_pc";
+
+  capPressure.postInputInitializationRecursive();
+  capPressure.initialize(); // to test all the checks
+  return capPressure;
+}
+
+CapillaryPressureBase & makeTableCapPressureTwoPhase2( string const & name, Group & parent )
+{
+  FunctionManager & functionManager = FunctionManager::getInstance();
+
+  // 1) First, define the tables
+
+  // 1D table, various interpolation methods
+  localIndex Naxis = 12;
+
+  // Setup table
+  array1d< real64_array > coordinates;
+  coordinates.resize( 1 );
+  coordinates[0].resize( Naxis );
+  coordinates[0][0] = 0.0;
+  coordinates[0][1] = 0.05;
+  coordinates[0][2] = 0.15;
+  coordinates[0][3] = 0.25;
+  coordinates[0][4] = 0.35;
+  coordinates[0][5] = 0.45;
+  coordinates[0][6] = 0.55;
+  coordinates[0][7] = 0.65;
+  coordinates[0][8] = 0.75;
+  coordinates[0][9] = 0.85;
+  coordinates[0][10] = 0.95;
+  coordinates[0][11] = 1.0;
+
+  real64_array values( Naxis );
+  values[0] = 195000.0;
+  values[1] = 135859.25;
+  values[2] = 73960.67;
+  values[3] = 50482.28;
+  values[4] = 36576.96;
+  values[5] = 26927.94;
+  values[6] = 19647;
+  values[7] = 13858.26;
+  values[8] = 9088.2;
+  values[9] = 5053.72;
+  values[10] = 1572.9;
+  values[11] = 0.0;
+
+  // localIndex const Naxis = 2;
+
+  // // Setup table
+  // array1d< real64_array > coordinates;
+  // coordinates.resize( 1 );
+  // coordinates[0].resize( Naxis );
+
+  // coordinates[0][0] = 0.0;
+  // coordinates[0][1] = 1.0;
+
+  // real64_array values( Naxis );
+  // values[0] = 129999.999994362;
+  // values[1] = 50000.0000139914;
+
+
+  TableFunction & table_w = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "water_pc" ) );
+  table_w.setTableCoordinates( coordinates, { units::Dimensionless } );
+  table_w.setTableValues( values, units::Pressure );
+  table_w.reInitializeFunction();
+
+  table_w.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  // 2) Then set up the constitutive model
+
+  TableCapillaryPressure & capPressure = parent.registerGroup< TableCapillaryPressure >( name );
+
+  string_array & phaseNames = capPressure.getReference< string_array >( CapillaryPressureBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  auto & waterTableName = capPressure.getReference< string >( TableCapillaryPressure::viewKeyStruct::wettingNonWettingCapPresTableNameString() );
+  waterTableName = "water_pc";
+
+  capPressure.postInputInitializationRecursive();
+  capPressure.initialize(); // to test all the checks
+  return capPressure;
+}
+
+CapillaryPressureBase & makeBrooksCoreyCapPressureTwoPhase1( string const & name, Group & parent )
+{
+  BrooksCoreyCapillaryPressure & capPressure = parent.registerGroup< BrooksCoreyCapillaryPressure >( name );
+
+  string_array & phaseNames = capPressure.getReference< string_array >( CapillaryPressureBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  array1d< real64 > & phaseMinSat = capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseMinVolumeFractionString() );
+  phaseMinSat.resize( 2 );
+  phaseMinSat[0] = phase0MinSat1; phaseMinSat[1] = phase1MinSat1;
+
+  array1d< real64 > & phaseCapPressureExpInv =
+    capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseCapPressureExponentInvString() );
+  phaseCapPressureExpInv.resize( 2 );
+  phaseCapPressureExpInv[0] = 4; phaseCapPressureExpInv[1] = 1;
+
+  array1d< real64 > & phaseEntryPressure = capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseEntryPressureString() );
+  phaseEntryPressure.resize( 2 );
+  phaseEntryPressure[0] = 0.75e5; phaseEntryPressure[1] = 0;
+
+  real64 & capPressureEpsilon = capPressure.getReference< real64 >( BrooksCoreyCapillaryPressure::viewKeyStruct::capPressureEpsilonString() );
+  capPressureEpsilon = 1.0e-8;
+
+  capPressure.postInputInitializationRecursive();
+  return capPressure;
+}
+
+CapillaryPressureBase & makeBrooksCoreyCapPressureTwoPhase2( string const & name, Group & parent )
+{
+  BrooksCoreyCapillaryPressure & capPressure = parent.registerGroup< BrooksCoreyCapillaryPressure >( name );
+
+  string_array & phaseNames = capPressure.getReference< string_array >( CapillaryPressureBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  array1d< real64 > & phaseMinSat = capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseMinVolumeFractionString() );
+  phaseMinSat.resize( 2 );
+  phaseMinSat[0] = phase0MinSat2; phaseMinSat[1] = phase1MinSat2;
+
+  array1d< real64 > & phaseCapPressureExpInv =
+    capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseCapPressureExponentInvString() );
+  phaseCapPressureExpInv.resize( 2 );
+  phaseCapPressureExpInv[0] = 4; phaseCapPressureExpInv[1] = 1;
+
+  array1d< real64 > & phaseEntryPressure = capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseEntryPressureString() );
+  phaseEntryPressure.resize( 2 );
+  phaseEntryPressure[0] = 0.5e5; phaseEntryPressure[1] = 0;
+
+  real64 & capPressureEpsilon = capPressure.getReference< real64 >( BrooksCoreyCapillaryPressure::viewKeyStruct::capPressureEpsilonString() );
+  capPressureEpsilon = 1e-8;
+
+  capPressure.postInputInitializationRecursive();
+  return capPressure;
+}
+
+RelativePermeabilityBase & makeBrooksCoreyRelPerm( string const & name, Group & parent )
+{
+  BrooksCoreyRelativePermeability & relPerm = parent.registerGroup< BrooksCoreyRelativePermeability >( name );
+
+  string_array & phaseNames = relPerm.getReference< string_array >( RelativePermeabilityBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  array1d< real64 > & phaseMinSat = relPerm.getReference< array1d< real64 > >( BrooksCoreyRelativePermeability::viewKeyStruct::phaseMinVolumeFractionString() );
+  phaseMinSat.resize( 2 );
+  phaseMinSat[0] = phase0MinSat1; phaseMinSat[1] = phase1MinSat1;
+
+  array1d< real64 > & phaseRelPermExp = relPerm.getReference< array1d< real64 > >( BrooksCoreyRelativePermeability::viewKeyStruct::phaseRelPermExponentString() );
+  phaseRelPermExp.resize( 2 );
+  phaseRelPermExp[0] = 2.0; phaseRelPermExp[1] = 2.0;
+
+  array1d< real64 > & phaseRelPermMaxVal = relPerm.getReference< array1d< real64 > >( BrooksCoreyRelativePermeability::viewKeyStruct::phaseRelPermMaxValueString() );
+  phaseRelPermMaxVal.resize( 2 );
+  phaseRelPermMaxVal[0] = 1.0; phaseRelPermMaxVal[1] = 1.0;
+
+  relPerm.postInputInitializationRecursive();
+  return relPerm;
+}
+
+class ImmiscibleInterfaceConditionsTest : public FluidModelTest< TwoPhaseImmiscibleFluid, 2 >
+{
+public:
+  ImmiscibleInterfaceConditionsTest(): state( std::make_unique< CommandLineOptions >( g_commandLineOptions )),
+    m_parent( "TestParentGroup", m_node )
+
+  {}
+
+protected:
+
+  static real64 constexpr time = 0.0;
+  static real64 constexpr dt = 1e4;
+  static real64 constexpr eps = std::numeric_limits< real64 >::epsilon();
+
+  GeosxState state;
+  ImmiscibleMultiphaseFlow *solver;
+  conduit::Node m_node;
+  dataRepository::Group m_parent;
+};
+
+real64 constexpr ImmiscibleInterfaceConditionsTest::time;
+real64 constexpr ImmiscibleInterfaceConditionsTest::dt;
+real64 constexpr ImmiscibleInterfaceConditionsTest::eps;
+
+
+
+TEST_F( ImmiscibleInterfaceConditionsTest, LocalNonlinearSolverConvergence )
+{
+
+  // using Base = FluidModelTest< TwoPhaseImmiscibleFluid, 2 >;
+  createFluid( "fluid", [this]( TwoPhaseImmiscibleFluid & fluid ){
+    makeTwoPhaseImmiscibleFluid( fluid );
+
+    // getting constitutive models:
+    RelativePermeabilityBase & relPerm = makeBrooksCoreyRelPerm( "relPerm", this->m_parent );
+    RelativePermeabilityBase * relPermPtr = &relPerm;
+    // CapillaryPressureBase & capPressure0 =  makeJFunctionCapPressureTwoPhase( "capPressure0", this->m_parent );
+    // CapillaryPressureBase * capPressurePtr0 = &capPressure0;
+
+    CapillaryPressureBase & capPressure0 =  makeTableCapPressureTwoPhase1( "capPressure0", this->m_parent );
+    CapillaryPressureBase * capPressurePtr0 = &capPressure0;
+
+    CapillaryPressureBase & capPressure1 =  makeTableCapPressureTwoPhase2( "capPressure1", this->m_parent );
+    CapillaryPressureBase * capPressurePtr1 = &capPressure1;
+    // CapillaryPressureBase & capPressure0 =  makeBrooksCoreyCapPressureTwoPhase1( "capPressure0", this->m_parent );
+    // CapillaryPressureBase * capPressurePtr0 = &capPressure0;
+
+    // CapillaryPressureBase & capPressure1 =  makeBrooksCoreyCapPressureTwoPhase2( "capPressure1", this->m_parent );
+    // CapillaryPressureBase * capPressurePtr1 = &capPressure1;
+
+    std::vector< RelativePermeabilityBase * > relPerms = {relPermPtr, relPermPtr};
+    std::vector< CapillaryPressureBase * > capPressures = {capPressurePtr0, capPressurePtr1};
+    std::vector< TwoPhaseImmiscibleFluid * > fluids = { &fluid, &fluid };
+    // real64 uT = 3.2864545889999906e-05;
+
+    // real64 uT = -3.3e-5;
+    real64 uT = 1e-17;
+// real64 uT = 1e-7;
+    stdVector< real64 > saturations = {0.2, 0.4};
+    stdVector< real64 > trappedSats1 = {phase0MinSat1, phase1MinSat1};
+    stdVector< real64 > trappedSats2 = {phase0MinSat2, phase1MinSat2};
+    stdVector< real64 > pressures = {1e7, 1e7};
+    stdVector< real64 > JFMultipliers = {45016.662822296035, 30011.108548197357};
+    stdVector< real64 > transHats = {1.9738466000000002e-12, 4.4411548500000007e-12};
+    stdVector< real64 > dTransHats_dP = {0.0, 0.0};
+    stdVector< real64 > gravCoefHats = {490.5, 490.5};
+    stdVector< real64 > gravCoefs = {465.97500000000002, 515.02499999999998};
+
+
+    std::vector< real64 > phi = {0.0, 0.0};
+    std::vector< real64 > grad_phi = {0.0, 0.0, 0.0, 0.0};
+
+    std::ofstream outFile( "local_solver_results.csv" );
+
+
+    // Write data to the file
+    outFile << "Si";
+    outFile << ",";
+    outFile << "Sj";
+    outFile << ",";
+    outFile << "Fw_alpha";
+    outFile << ",";
+    outFile << "Fn_alpha";
+    outFile << ",";
+    outFile << "Residual_initial";
+    outFile << ",";
+    outFile << "Pc_int";
+    outFile << ",";
+    outFile << "Residual";
+    outFile << ",";
+    outFile << "newton";
+    outFile << std::endl;
+
+    real64 const start_sat = 0.0;
+    real64 const end_sat   = 1.0;
+    real64 const dS        = 1e-2;
+    real64 Si = 0.0;
+    real64 Sj = 0.9;
+
+    // for( real64 Si = start_sat; Si <= end_sat + 1e-8; Si += dS )
+    // {
+    //   for( real64 Sj = start_sat; Sj <= end_sat + 1e-8; Sj += dS )
+    //   {
+    saturations[0] = Si;
+    saturations[1] = Sj;
+
+    auto t0 = std::chrono::high_resolution_clock::now();
+
+    // Define missing arguments for the updated signature
+    stdVector< real64 > cellCenterDuT = { 0.0, 0.0 };
+    stdVector< real64 > cellCenterDens = { 0.0, 0.0 };
+    stdVector< real64 > cellCenterDens_dP = { 0.0, 0.0 };
+    std::vector< real64 > grad_phi_P = { 0.0, 0.0 };
+    std::vector< real64 > grad_phi_S = { 0.0, 0.0 };
+    bool converged;
+
+    // Call the GEOS local solver
+    geos::immiscibleMultiphaseKernels::local_solver( uT, saturations, pressures, JFMultipliers, trappedSats1, trappedSats2, transHats, dTransHats_dP, gravCoefHats, gravCoefs,
+                                                     cellCenterDuT, cellCenterDens, cellCenterDens_dP,
+                                                     relPerms, capPressures, fluids, phi, grad_phi_P, grad_phi_S, converged );
+
+    auto t1 = std::chrono::high_resolution_clock::now();
+    std::chrono::duration< double > elapsed = t1 - t0;
+    std::cout << "Local solver time: " << elapsed.count() << " s" << std::endl;
+
+
+    // Write data to the file
+    outFile << GEOS_FMT( "{:10.10e}", saturations[0] );
+    outFile << GEOS_FMT( ",{:10.10e}", saturations[1] );
+    outFile << GEOS_FMT( ",{:10.10e}", phi[0] );
+    outFile << GEOS_FMT( ",{:10.10e}", phi[1] );
+    outFile << GEOS_FMT( ",{:10.10e}", grad_phi_P[0] );
+    outFile << GEOS_FMT( ",{:10.10e}", grad_phi_P[1] );
+    outFile << GEOS_FMT( ",{:10.10e}", grad_phi_S[0] );
+    outFile << GEOS_FMT( ",{:10.10e}", grad_phi_S[1] );
+    outFile << std::endl;
+    phi[0] = 0;
+    phi[1] = 0;
+    grad_phi_P[0] = 0;
+    grad_phi_P[1] = 0;
+    grad_phi_S[0] = 0;
+    grad_phi_S[1] = 0;
+
+//   }
+// }
+
+    outFile.close();
+
+  } );
+}
+
+int main( int argc, char * *argv )
+{
+  ::testing::InitGoogleTest( &argc, argv );
+  g_commandLineOptions = *geos::basicSetup( argc, argv );
+  int const result = RUN_ALL_TESTS();
+  geos::basicCleanup();
+  return result;
+}
+
+// maybe needed later on
+// TEST_F( CapillaryPressureTest, numericalDerivatives_jFunctionCapPressureTwoPhase )
+// {
+//   initialize( makeJFunctionCapPressureTwoPhase( "capPressure", m_parent ) );
+
+//   // here, we have to apply a special treatment to this test
+//   // to make sure that the J-function multiplier is initialized using initializeRockState
+//   // this requires calling allocateConstitutiveData in advance (it will be called again later, in the "test" function)
+
+//   // setup some values for porosity and permeability
+//   array2d< real64 > porosity;
+//   porosity.resize( 1, 1 );
+//   porosity[0][0] = 0.13496794266569806;
+//   array3d< real64 > permeability;
+//   permeability.resize( 1, 1, 3 );
+//   permeability[0][0][0] = 0.1722194e-15;
+//   permeability[0][0][1] = 0.3423156e-15;
+//   permeability[0][0][2] = 0.2324191e-15;
+
+//   // initialize the J-function multiplier (done on GPU if GPU is available)
+//   m_model->allocateConstitutiveData( m_parent, 1 );
+//   m_model->initializeRockState( porosity.toViewConst(), permeability.toViewConst() );
+
+//   // move the multiplier back to the CPU since the test is performed on the CPU
+//   auto & jFuncMultiplier =
+//     m_model->getReference< array2d< real64 > >( fields::cappres::jFuncMultiplier::key() );
+//   jFuncMultiplier.move( hostMemorySpace, false );
+
+//   // we are ready to proceed to the test
+
+//   real64 const eps = std::sqrt( std::numeric_limits< real64 >::epsilon() );
+//   real64 const tol = 1e-4;
+
+//   real64 const start_sat = 0.3;
+//   real64 const end_sat   = 0.9;
+//   real64 const dS        = 1e-1;
+//   array1d< real64 > sat( 2 );
+//   sat[0] = start_sat; sat[1] = 1-sat[0];
+//   while( sat[0] <= end_sat )
+//   {
+//     test( sat, eps, tol );
+//     sat[0] += dS;
+//     sat[1] = 1 - sat[0];
+//   }
+
+// }
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/CMakeLists.txt b/src/coreComponents/physicsSolvers/fluidFlow/CMakeLists.txt
index 6eb55e9775a..b0bcc0bd271 100644
--- a/src/coreComponents/physicsSolvers/fluidFlow/CMakeLists.txt
+++ b/src/coreComponents/physicsSolvers/fluidFlow/CMakeLists.txt
@@ -29,8 +29,6 @@ set( fluidFlowSolvers_headers
      ImmiscibleMultiphaseFlow.hpp
      ImmiscibleMultiphaseFlowFields.hpp
      LogLevelsInfo.hpp
-     ReactiveCompositionalMultiphaseOBL.hpp
-     ReactiveCompositionalMultiphaseOBLFields.hpp
      SourceFluxStatistics.hpp
      SinglePhaseBase.hpp
      SinglePhaseBaseFields.hpp
@@ -65,18 +63,6 @@ set( fluidFlowSolvers_headers
      kernels/singlePhase/ThermalFluxComputeKernel.hpp
      kernels/singlePhase/proppant/ProppantBaseKernels.hpp
      kernels/singlePhase/proppant/ProppantFluxKernels.hpp
-     kernels/singlePhase/reactive/AccumulationKernels.hpp
-     kernels/singlePhase/reactive/DirichletFluxComputeKernel.hpp
-     kernels/singlePhase/reactive/FluidUpdateKernel.hpp
-     kernels/singlePhase/reactive/FluxComputeKernel.hpp
-     kernels/singlePhase/reactive/KernelLaunchSelectors.hpp
-     kernels/singlePhase/reactive/ReactionUpdateKernel.hpp
-     kernels/singlePhase/reactive/ResidualNormKernel.hpp
-     kernels/singlePhase/reactive/SourceFluxComputeKernel.hpp
-     kernels/singlePhase/reactive/ThermalAccumulationKernels.hpp
-     kernels/singlePhase/reactive/ThermalDirichletFluxComputeKernel.hpp
-     kernels/singlePhase/reactive/ThermalFluxComputeKernel.hpp
-     kernels/singlePhase/reactive/ThermalSourceFluxComputeKernel.hpp
      kernels/compositional/AccumulationKernel.hpp
      kernels/compositional/AquiferBCKernel.hpp
      kernels/compositional/PPUPhaseFlux.hpp
@@ -104,7 +90,6 @@ set( fluidFlowSolvers_headers
      kernels/compositional/PotGrad.hpp
      kernels/compositional/PPUPhaseFlux.hpp
      kernels/compositional/PropertyKernelBase.hpp
-     kernels/compositional/ReactiveCompositionalMultiphaseOBLKernels.hpp
      kernels/compositional/RelativePermeabilityUpdateKernel.hpp
      kernels/compositional/ResidualNormKernel.hpp
      kernels/compositional/SolidInternalEnergyUpdateKernel.hpp
@@ -145,14 +130,12 @@ set( fluidFlowSolvers_sources
      CompositionalMultiphaseStatistics.cpp
      CompositionalMultiphaseHybridFVM.cpp
      ImmiscibleMultiphaseFlow.cpp
-     ReactiveCompositionalMultiphaseOBL.cpp
      FlowSolverBase.cpp
      SinglePhaseBase.cpp
      SinglePhaseStatistics.cpp
      SinglePhaseFVM.cpp
      SinglePhaseHybridFVM.cpp
      SinglePhaseProppantBase.cpp
-     SinglePhaseReactiveTransport.cpp
      SourceFluxStatistics.cpp
      StencilDataCollection.cpp
      kernels/singlePhase/proppant/ProppantFluxKernels.cpp
@@ -174,8 +157,10 @@ file( READ "${CMAKE_CURRENT_LIST_DIR}/kernelSpecs.json" kernelSpecs )
 set( kernelTemplateFileList "" )
 
 # Keep only the templates that are unrelated to hybrid flux/dirichlet
-list( APPEND kernelTemplateFileList
-      ReactiveCompositionalMultiphaseOBLKernels.cpp.template )
+if( ENABLE_HPCREACT AND EXISTS "${CMAKE_CURRENT_SOURCE_DIR}/../constitutive/HPCReact/CMakeLists.txt" )
+  list( APPEND kernelTemplateFileList
+        ReactiveCompositionalMultiphaseOBLKernels.cpp.template )
+endif()
 
 foreach( kernelTemplateFile ${kernelTemplateFileList} )
   get_filename_component( jsonKey ${kernelTemplateFile} NAME_WE )
@@ -188,6 +173,31 @@ foreach( kernelTemplateFile ${kernelTemplateFileList} )
   list(APPEND fluidFlowSolvers_sources ${sourceFiles})
 endforeach()
 
+# Conditionally add reactive transport files when HPCReact is available
+if( ENABLE_HPCREACT AND EXISTS "${CMAKE_CURRENT_SOURCE_DIR}/../constitutive/HPCReact/CMakeLists.txt" )
+  list( APPEND fluidFlowSolvers_headers
+       ReactiveCompositionalMultiphaseOBL.hpp
+       ReactiveCompositionalMultiphaseOBLFields.hpp
+       kernels/singlePhase/reactive/AccumulationKernels.hpp
+       kernels/singlePhase/reactive/DirichletFluxComputeKernel.hpp
+       kernels/singlePhase/reactive/FluidUpdateKernel.hpp
+       kernels/singlePhase/reactive/FluxComputeKernel.hpp
+       kernels/singlePhase/reactive/KernelLaunchSelectors.hpp
+       kernels/singlePhase/reactive/ReactionUpdateKernel.hpp
+       kernels/singlePhase/reactive/ResidualNormKernel.hpp
+       kernels/singlePhase/reactive/SourceFluxComputeKernel.hpp
+       kernels/singlePhase/reactive/ThermalAccumulationKernels.hpp
+       kernels/singlePhase/reactive/ThermalDirichletFluxComputeKernel.hpp
+       kernels/singlePhase/reactive/ThermalFluxComputeKernel.hpp
+       kernels/singlePhase/reactive/ThermalSourceFluxComputeKernel.hpp
+       kernels/compositional/ReactiveCompositionalMultiphaseOBLKernels.hpp
+       SinglePhaseReactiveTransport.hpp )
+  
+  list( APPEND fluidFlowSolvers_sources
+       ReactiveCompositionalMultiphaseOBL.cpp
+       SinglePhaseReactiveTransport.cpp )
+endif()
+
 # TODO: The two kernels below have non-matching file names and JSON keys.
 #       Either fix them to follow pattern, or come up with another mechanism.
 
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.cpp b/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.cpp
index a198a78cb17..ec169a7e330 100644
--- a/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.cpp
+++ b/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.cpp
@@ -17,31 +17,34 @@
  * @file ImmiscibleMultiphaseFlow.cpp
  */
 
-#include "ImmiscibleMultiphaseFlow.hpp"
-
-#include "FlowSolverBaseFields.hpp"
-#include "physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlowFields.hpp"
-#include "physicsSolvers/PhysicsSolverBaseKernels.hpp"
-#include "physicsSolvers/fluidFlow/CompositionalMultiphaseUtilities.hpp"
-#include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp"
-#include "physicsSolvers/fluidFlow/kernels/compositional/RelativePermeabilityUpdateKernel.hpp"
-#include "physicsSolvers/fluidFlow/kernels/compositional/CapillaryPressureUpdateKernel.hpp"
-#include "constitutive/capillaryPressure/CapillaryPressureSelector.hpp"
-#include "constitutive/relativePermeability/RelativePermeabilitySelector.hpp"
-
-#include "fieldSpecification/EquilibriumInitialCondition.hpp"
-#include "fieldSpecification/SourceFluxBoundaryCondition.hpp"
-#include "physicsSolvers/fluidFlow/SourceFluxStatistics.hpp"
-#include "physicsSolvers/LogLevelsInfo.hpp"
-
-#include "constitutive/ConstitutivePassThru.hpp"
-#include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluid.hpp"
-
-#include <cmath>
-
-#if defined( __INTEL_COMPILER )
-#pragma GCC optimize "O0"
-#endif
+ #include "ImmiscibleMultiphaseFlow.hpp"
+
+ #include "FlowSolverBaseFields.hpp"
+ #include "physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlowFields.hpp"
+ #include "physicsSolvers/PhysicsSolverBaseKernels.hpp"
+ #include "physicsSolvers/fluidFlow/CompositionalMultiphaseUtilities.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/CapillaryPressureUpdateKernel.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/compositional/ThermalAccumulationKernel.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/compositional/RelativePermeabilityUpdateKernel.hpp"
+ #include "constitutive/ConstitutiveManager.hpp"
+ #include "constitutive/capillaryPressure/CapillaryPressureFields.hpp"
+ #include "constitutive/capillaryPressure/CapillaryPressureSelector.hpp"
+ #include "constitutive/relativePermeability/RelativePermeabilitySelector.hpp"
+
+ #include "fieldSpecification/EquilibriumInitialCondition.hpp"
+ #include "fieldSpecification/SourceFluxBoundaryCondition.hpp"
+ #include "physicsSolvers/fluidFlow/SourceFluxStatistics.hpp"
+ #include "physicsSolvers/LogLevelsInfo.hpp"
+
+ #include "constitutive/ConstitutivePassThru.hpp"
+ #include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluid.hpp"
+
+ #include <cmath>
+
+ #if defined( __INTEL_COMPILER )
+ #pragma GCC optimize "O0"
+ #endif
 
 namespace geos
 {
@@ -90,7 +93,12 @@ ImmiscibleMultiphaseFlow::ImmiscibleMultiphaseFlow( const string & name,
     setSizedFromParent( 0 ).
     setInputFlag( InputFlags::OPTIONAL ).
     setApplyDefaultValue( 0.2 ).
-    setDescription( "Target (absolute) change in the phase volume fraction within a single time step." );
+    setDescription( "Target (absolute) change in phase volume fraction in a time step" );
+
+  this->registerWrapper( viewKeyStruct::interfaceFaceSetNamesString(),
+                         &m_interfaceFaceSetNames ).
+    setInputFlag( InputFlags::OPTIONAL ).
+    setDescription( "Names of the interface face sets" );
 }
 
 void ImmiscibleMultiphaseFlow::postInputInitialization()
@@ -169,7 +177,7 @@ void ImmiscibleMultiphaseFlow::registerDataOnMesh( Group & meshBodies )
         reference().resizeDimension< 1 >( m_numPhases );
 
       subRegion.registerField< dPhaseMobility >( getName() ).
-        reference().resizeDimension< 1, 2 >( m_numPhases, m_numPhases ); // dP, dS
+        reference().resizeDimension< 1, 2 >( m_numPhases, m_numPhases );  // dP, dS
 
     } );
 
@@ -203,6 +211,132 @@ void ImmiscibleMultiphaseFlow::initializePreSubGroups()
       temp.setValues< parallelHostPolicy >( m_inputTemperature );
     } );
   } );
+
+  // ***** Create FaceElements *****
+  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                               MeshLevel & meshLevel,
+                                                               string_array const & GEOS_UNUSED_PARAM( regionNames ))
+  {
+
+    FaceManager const & faceManager = meshLevel.getFaceManager();
+    Group const & faceSetGroup = faceManager.sets();
+    ElementRegionManager & elemManager = meshLevel.getElemManager();
+    m_interfaceConstitutivePairs.resize( m_interfaceFaceSetNames.size() );
+
+    // this is the FaceElement Level
+    for( size_t surfaceRegionIndex=0; surfaceRegionIndex < m_interfaceFaceSetNames.size(); ++surfaceRegionIndex )
+    {
+      string const & faceSetName = m_interfaceFaceSetNames[surfaceRegionIndex];
+      SortedArrayView< localIndex const > const & faceSet = faceSetGroup.getReference< SortedArray< localIndex > >( faceSetName );
+      SurfaceElementRegion & faceRegion = elemManager.getRegion< SurfaceElementRegion >( faceSetName );
+
+      for( localIndex const faceIndex : faceSet )
+      {
+        localIndex const faceIndices[2] = { faceIndex, faceIndex };
+        faceRegion.addToSurfaceMesh( &faceManager, faceIndices );
+      }
+
+      FaceElementSubRegion const & faceSubRegion = faceRegion.getUniqueSubRegion< FaceElementSubRegion >();
+      FixedToManyElementRelation const & faceElementsToCells = faceSubRegion.getToCellRelation();
+
+      std::function< std::tuple< CellElementSubRegion *, CellElementSubRegion * >(localIndex) > getSubregions = [&]( localIndex surfaceSubRegionIndex ) -> std::tuple< CellElementSubRegion *,
+                                                                                                                                                                       CellElementSubRegion * >
+      {
+
+        int regionIdx0 = faceElementsToCells.m_toElementRegion[surfaceSubRegionIndex][0];
+        int regionIdx1 = faceElementsToCells.m_toElementRegion[surfaceSubRegionIndex][1];
+        int subRegionIdx0 = faceElementsToCells.m_toElementSubRegion[surfaceSubRegionIndex][0];
+        int subRegionIdx1 = faceElementsToCells.m_toElementSubRegion[surfaceSubRegionIndex][1];
+
+        CellElementRegion & region0 = elemManager.getRegion< CellElementRegion >( regionIdx0 );
+        CellElementRegion & region1 = elemManager.getRegion< CellElementRegion >( regionIdx1 );
+
+        CellElementSubRegion * subRegion0 = &region0.getSubRegion< CellElementSubRegion >( subRegionIdx0 );
+        CellElementSubRegion * subRegion1 = &region1.getSubRegion< CellElementSubRegion >( subRegionIdx1 );
+        return std::make_tuple( subRegion0, subRegion1 );
+      };
+
+      //  std::tuple< CellElementSubRegion *, CellElementSubRegion * > subRegionPair = getSubregions( surfaceRegionIndex );
+      //  CellElementSubRegion * subRegion0 = std::get< 0 >( subRegionPair );
+      //  CellElementSubRegion * subRegion1 = std::get< 1 >( subRegionPair );
+
+      //  // get constitutives by type and name: relPerms, capPressures, Fluids (three pointers)
+      //  std::string & relPermName0 = subRegion0->getReference< std::string >( viewKeyStruct::relPermNamesString());
+      //  std::string & relPermName1 = subRegion1->getReference< std::string >( viewKeyStruct::relPermNamesString());
+      //  RelativePermeabilityBase * relPerm0 = &getConstitutiveModel< RelativePermeabilityBase >( *subRegion0, relPermName0 );
+      //  RelativePermeabilityBase * relPerm1 = &getConstitutiveModel< RelativePermeabilityBase >( *subRegion1, relPermName1 );
+
+      //  std::string & cappresName0 = subRegion0->getReference< std::string >( viewKeyStruct::capPressureNamesString());
+      //  std::string & cappresName1 = subRegion1->getReference< std::string >( viewKeyStruct::capPressureNamesString());
+      //  CapillaryPressureBase * capPressure0 = &getConstitutiveModel< CapillaryPressureBase >( *subRegion0, cappresName0 );
+      //  CapillaryPressureBase * capPressure1 = &getConstitutiveModel< CapillaryPressureBase >( *subRegion1, cappresName1 );
+
+      //  std::string & fluidName0 = subRegion0->getReference< std::string >( viewKeyStruct::fluidNamesString() );
+      //  std::string & fluidName1 = subRegion1->getReference< std::string >( viewKeyStruct::fluidNamesString() );
+
+      //  TwoPhaseImmiscibleFluid * fluid0 = &getConstitutiveModel< TwoPhaseImmiscibleFluid >( *subRegion0, fluidName0 );
+      //  TwoPhaseImmiscibleFluid * fluid1 = &getConstitutiveModel< TwoPhaseImmiscibleFluid >( *subRegion1, fluidName1 );
+
+      //  m_interfaceConstitutivePairs[surfaceRegionIndex][0] = std::make_tuple( relPerm0, capPressure0, fluid0 );
+      //  m_interfaceConstitutivePairs[surfaceRegionIndex][1] = std::make_tuple( relPerm1, capPressure1, fluid1 );
+      // Find a representative face element in this surface region with two adjacent cells
+      localIndex fei = -1;
+
+// Prefer face element 0 if valid; otherwise scan
+      if( faceElementsToCells.size() > 0 )
+      {
+        // Check if face element 0 has two adjacent cells
+        if( faceElementsToCells.m_toElementRegion[0].size() >= 2 )
+        {
+          fei = 0;
+        }
+        else
+        {
+          // Scan to find the first interior face element with two neighbors
+          for( localIndex i = 1; i < faceElementsToCells.size(); ++i )
+          {
+            if( faceElementsToCells.m_toElementRegion[i].size() >= 2 )
+            {
+              fei = i;
+              break;
+            }
+          }
+        }
+      }
+
+// If no valid face element, skip this surface region
+      if( fei < 0 )
+      {
+        continue;
+      }
+
+      std::tuple< CellElementSubRegion *, CellElementSubRegion * > subRegionPair = getSubregions( fei );
+      CellElementSubRegion * subRegion0 = std::get< 0 >( subRegionPair );
+      CellElementSubRegion * subRegion1 = std::get< 1 >( subRegionPair );
+
+// get constitutives by type and name: relPerms, capPressures, Fluids (three pointers)
+      std::string & relPermName0 = subRegion0->getReference< std::string >( viewKeyStruct::relPermNamesString());
+      std::string & relPermName1 = subRegion1->getReference< std::string >( viewKeyStruct::relPermNamesString());
+      RelativePermeabilityBase * relPerm0 = &getConstitutiveModel< RelativePermeabilityBase >( *subRegion0, relPermName0 );
+      RelativePermeabilityBase * relPerm1 = &getConstitutiveModel< RelativePermeabilityBase >( *subRegion1, relPermName1 );
+
+      std::string & cappresName0 = subRegion0->getReference< std::string >( viewKeyStruct::capPressureNamesString());
+      std::string & cappresName1 = subRegion1->getReference< std::string >( viewKeyStruct::capPressureNamesString());
+      CapillaryPressureBase * capPressure0 = &getConstitutiveModel< CapillaryPressureBase >( *subRegion0, cappresName0 );
+      CapillaryPressureBase * capPressure1 = &getConstitutiveModel< CapillaryPressureBase >( *subRegion1, cappresName1 );
+
+      std::string & fluidName0 = subRegion0->getReference< std::string >( viewKeyStruct::fluidNamesString() );
+      std::string & fluidName1 = subRegion1->getReference< std::string >( viewKeyStruct::fluidNamesString() );
+
+      TwoPhaseImmiscibleFluid * fluid0 = &getConstitutiveModel< TwoPhaseImmiscibleFluid >( *subRegion0, fluidName0 );
+      TwoPhaseImmiscibleFluid * fluid1 = &getConstitutiveModel< TwoPhaseImmiscibleFluid >( *subRegion1, fluidName1 );
+
+      m_interfaceConstitutivePairs[surfaceRegionIndex][0] = std::make_tuple( relPerm0, capPressure0, fluid0 );
+      m_interfaceConstitutivePairs[surfaceRegionIndex][1] = std::make_tuple( relPerm1, capPressure1, fluid1 );
+
+    }
+  } );
+
 }
 
 
@@ -265,7 +399,8 @@ void ImmiscibleMultiphaseFlow::updateCapPressureModel( ObjectManagerBase & dataG
     {
       typename TYPEOFREF( castedCapPres ) ::KernelWrapper capPresWrapper = castedCapPres.createKernelWrapper();
 
-      isothermalCompositionalMultiphaseBaseKernels::
+      // isothermalCompositionalMultiphaseBaseKernels::
+      immiscibleMultiphaseKernels::
         CapillaryPressureUpdateKernel::
         launch< parallelDevicePolicy<> >( dataGroup.size(),
                                           capPresWrapper,
@@ -373,7 +508,7 @@ void ImmiscibleMultiphaseFlow::initializeFluidState( MeshLevel & mesh,
       getConstitutiveModel< PermeabilityBase >( subRegion, subRegion.template getReference< string >( viewKeyStruct::permeabilityNamesString() ) );
     permeabilityModel.scaleHorizontalPermeability( netToGross );
     porousSolid.scaleReferencePorosity( netToGross );
-    saveConvergedState( subRegion ); // necessary for a meaningful porosity update in sequential schemes
+    saveConvergedState( subRegion );  // necessary for a meaningful porosity update in sequential schemes
     updatePorosityAndPermeability( subRegion );
 
     // Now, we initialize and update each constitutive model one by one
@@ -402,9 +537,9 @@ void ImmiscibleMultiphaseFlow::initializeFluidState( MeshLevel & mesh,
     string const & relpermName = subRegion.template getReference< string >( viewKeyStruct::relPermNamesString() );
     RelativePermeabilityBase & relPermMaterial =
       getConstitutiveModel< RelativePermeabilityBase >( subRegion, relpermName );
-    relPermMaterial.saveConvergedPhaseVolFractionState( phaseVolFrac ); // this needs to happen before calling updateRelPermModel
+    relPermMaterial.saveConvergedPhaseVolFractionState( phaseVolFrac );  // this needs to happen before calling updateRelPermModel
     updateRelPermModel( subRegion );
-    relPermMaterial.saveConvergedState(); // this needs to happen after calling updateRelPermModel
+    relPermMaterial.saveConvergedState();  // this needs to happen after calling updateRelPermModel
 
     // 4.4 Then, we initialize/update the capillary pressure model
     //
@@ -424,7 +559,7 @@ void ImmiscibleMultiphaseFlow::initializeFluidState( MeshLevel & mesh,
       string const & capPressureName = subRegion.template getReference< string >( viewKeyStruct::capPressureNamesString() );
       CapillaryPressureBase const & capPressureMaterial =
         getConstitutiveModel< CapillaryPressureBase >( subRegion, capPressureName );
-      capPressureMaterial.initializeRockState( porosity, permeability ); // this needs to happen before calling updateCapPressureModel
+      capPressureMaterial.initializeRockState( porosity, permeability );  // this needs to happen before calling updateCapPressureModel
       updateCapPressureModel( subRegion );
     }
 
@@ -473,6 +608,48 @@ void ImmiscibleMultiphaseFlow::initializePostInitialConditionsPreSubGroups()
     CommunicationTools::getInstance().synchronizeFields( fieldsToBeSync, mesh, domain.getNeighbors(), false );
   } );
 
+  // Retrieve the numerical methods and finite volume manager
+  FiniteVolumeManager const & fvManager = domain.getNumericalMethodManager().getFiniteVolumeManager();
+  FluxApproximationBase const & fluxApprox = fvManager.getFluxApproximation( m_discretizationName );
+  const geos::string flux_approximation_name = fluxApprox.getName();
+
+  // Clear the existing mapping between connector indices and interface region indices
+  m_interfaceRegionByConnector.clear();
+  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( std::string const &,
+                                                               MeshLevel & meshLevel,
+                                                               string_array const & GEOS_UNUSED_PARAM( regionNames ))
+  {
+    // Access the face manager and retrieve the face set group for the current mesh level
+    FaceManager const & faceManager = meshLevel.getFaceManager();
+    Group const & faceSetGroup = faceManager.sets();
+
+    // Access the connector indices map (face index → connector index)
+    Group & stencilGroup =
+      meshLevel.getGroup( FluxApproximationBase::groupKeyStruct::stencilMeshGroupString())
+        .getGroup( flux_approximation_name );
+    CellElementStencilTPFA & stencil =
+      stencilGroup.getReference< CellElementStencilTPFA >(
+        FluxApproximationBase::viewKeyStruct::cellStencilString());
+    unordered_map< localIndex, localIndex > const & connectorIndices = stencil.getConnectorIndices();
+
+    // for all interface face sets to map connector indices to their corresponding interface region indices
+    for( size_t surfaceRegionIndex = 0; surfaceRegionIndex < m_interfaceFaceSetNames.size(); ++surfaceRegionIndex )
+    {
+      // Iterate over each face and associate its connector index
+      std::string const & faceSetName = m_interfaceFaceSetNames[surfaceRegionIndex];
+      for( localIndex kf : faceSetGroup.getReference< SortedArray< localIndex > >( faceSetName ))
+      {
+        auto it = connectorIndices.find( kf );
+        if( it != connectorIndices.end())
+        {
+          // Map the connector index to the corresponding surface region index
+          m_interfaceRegionByConnector[it->second] = surfaceRegionIndex;
+        }
+      }
+    }
+  } );
+
+
   initializeState( domain );
 }
 
@@ -582,7 +759,7 @@ void ImmiscibleMultiphaseFlow::assembleAccumulationTerm( DomainPartition & domai
 }
 
 void ImmiscibleMultiphaseFlow::assembleFluxTerms( real64 const dt,
-                                                  DomainPartition const & domain,
+                                                  DomainPartition & domain,
                                                   DofManager const & dofManager,
                                                   CRSMatrixView< real64, globalIndex const > const & localMatrix,
                                                   arrayView1d< real64 > const & localRhs ) const
@@ -595,30 +772,90 @@ void ImmiscibleMultiphaseFlow::assembleFluxTerms( real64 const dt,
 
   string const & dofKey = dofManager.getKey( viewKeyStruct::elemDofFieldString() );
 
+
   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&] ( string const &,
-                                                                MeshLevel const & mesh,
-                                                                string_array const & )
+                                                                MeshLevel & mesh,
+                                                                string_array const & regionNames )
   {
-    fluxApprox.forAllStencils( mesh, [&]( auto & stencil )
+    if( m_hasCapPressure )
     {
-      typename TYPEOFREF( stencil ) ::KernelWrapper stencilWrapper = stencil.createKernelWrapper();
-      immiscibleMultiphaseKernels::
-        FluxComputeKernelFactory::createAndLaunch< parallelDevicePolicy<> >( m_numPhases,
-                                                                             dofManager.rankOffset(),
-                                                                             dofKey,
-                                                                             m_hasCapPressure,
-                                                                             m_useTotalMassEquation,
-                                                                             m_gravityDensityScheme == GravityDensityScheme::PhasePresence,
-                                                                             getName(),
-                                                                             mesh.getElemManager(),
-                                                                             stencilWrapper,
-                                                                             dt,
-                                                                             localMatrix.toViewConstSizes(),
-                                                                             localRhs.toView() );
-    } );
+      mesh.getElemManager().forElementSubRegions( regionNames,
+                                                  [&]( localIndex const,
+                                                       ElementSubRegionBase & subRegion )  // Check if you need this.
+      {
+        //  // Capillary pressure wrapper
+        //  string const & cappresName = subRegion.getReference< string >( viewKeyStruct::capPressureNamesString() );
+        //  BrooksCoreyCapillaryPressure & capPressure = getConstitutiveModel< BrooksCoreyCapillaryPressure >( subRegion, cappresName );
+        //  CapillaryPressureBase * capPressure1 = &getConstitutiveModel< CapillaryPressureBase >( subRegion, cappresName );
+        //  BrooksCoreyCapillaryPressure::KernelWrapper capPresWrapper = capPressure.createKernelWrapper();
+
+        //  // Relative permeability wrapper
+        //  string const & relPermName = subRegion.getReference< string >( viewKeyStruct::relPermNamesString() );
+        //  BrooksCoreyRelativePermeability & relPerm = getConstitutiveModel< BrooksCoreyRelativePermeability >( subRegion, relPermName );
+        //  RelativePermeabilityBase  * relPerm1 = &getConstitutiveModel< RelativePermeabilityBase >( subRegion, relPermName );
+        //  BrooksCoreyRelativePermeability::KernelWrapper relPermWrapper = relPerm.createKernelWrapper();
+
+        //  // fluid
+        //  string const & fluidName = subRegion.getReference< string >( viewKeyStruct::fluidNamesString() );
+        //  TwoPhaseImmiscibleFluid * fluid = &getConstitutiveModel< TwoPhaseImmiscibleFluid >( subRegion, fluidName );
+
+        //  // m_interfaceConstitutivePairs[0][0] = std::make_tuple( relPerm1, capPressure1, fluid );
+        //  // m_interfaceConstitutivePairs[0][1] = std::make_tuple( relPerm1, capPressure1, fluid );
+
+        //  auto interfaceConstitutivePairs_temp = std::make_tuple( relPerm1, capPressure1, fluid );
+
+        fluxApprox.forAllStencils( mesh, [&]( auto & stencil )
+        {
+          typename TYPEOFREF( stencil ) ::KernelWrapper stencilWrapper = stencil.createKernelWrapper();
+          immiscibleMultiphaseKernels::
+            FluxComputeKernelFactory::createAndLaunch< parallelDevicePolicy<> >( m_numPhases,
+                                                                                 dofManager.rankOffset(),
+                                                                                 dofKey,
+                                                                                 m_hasCapPressure,
+                                                                                 m_useTotalMassEquation,
+                                                                                 m_gravityDensityScheme == GravityDensityScheme::PhasePresence,
+                                                                                 getName(),
+                                                                                 mesh.getElemManager(),
+                                                                                 stencilWrapper,
+                                                                                 // capPresWrapper,
+                                                                                 // relPermWrapper,
+                                                                                 m_interfaceFaceSetNames,
+                                                                                 m_interfaceConstitutivePairs,
+                                                                                 m_interfaceRegionByConnector,
+                                                                                 // interfaceConstitutivePairs_temp,
+                                                                                 subRegion,
+                                                                                 dt,
+                                                                                 localMatrix.toViewConstSizes(),
+                                                                                 localRhs.toView() );
+        } );
+      } );
+    }
+    else
+    {
+      fluxApprox.forAllStencils( mesh, [&]( auto & stencil )
+      {
+        typename TYPEOFREF( stencil ) ::KernelWrapper stencilWrapper = stencil.createKernelWrapper();
+        immiscibleMultiphaseKernels::
+          FluxComputeKernelFactory::createAndLaunch< parallelDevicePolicy<> >( m_numPhases,
+                                                                               dofManager.rankOffset(),
+                                                                               dofKey,
+                                                                               m_hasCapPressure,
+                                                                               m_useTotalMassEquation,
+                                                                               m_gravityDensityScheme == GravityDensityScheme::PhasePresence,
+                                                                               getName(),
+                                                                               mesh.getElemManager(),
+                                                                               stencilWrapper,
+                                                                               dt,
+                                                                               localMatrix.toViewConstSizes(),
+                                                                               localRhs.toView() );
+      } );
+    }
+
   } );
 }
 
+// Ryan: Looks like this will need to be overwritten as well...
+// I have left the CompositionalMultiphaseFVM implementation for reference
 void ImmiscibleMultiphaseFlow::setupDofs( DomainPartition const & domain,
                                           DofManager & dofManager ) const
 {
@@ -730,7 +967,7 @@ bool ImmiscibleMultiphaseFlow::validateDirichletBC( DomainPartition & domain,
         bcConsistent = false;
         GEOS_WARNING( BCMessage::invalidComponentIndex( comp, fs.getName(),
                                                         fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() ) );
-        return; // can't check next part with invalid component id
+        return;  // can't check next part with invalid component id
       }
 
       ComponentMask< MAX_NP > & compMask = subRegionSetMap[setName];
@@ -1014,7 +1251,7 @@ void ImmiscibleMultiphaseFlow::applySourceFluxBC( real64 const time,
           return;
         }
 
-        real64 const rhsValue = rhsContributionArrayView[a] / sizeScalingFactor; // scale the contribution by the sizeScalingFactor here!
+        real64 const rhsValue = rhsContributionArrayView[a] / sizeScalingFactor;  // scale the contribution by the sizeScalingFactor here!
         massProd += rhsValue;
         if( useTotalMassEquation > 0 )
         {
@@ -1023,7 +1260,7 @@ void ImmiscibleMultiphaseFlow::applySourceFluxBC( real64 const time,
           localRhs[totalMassBalanceRow] += rhsValue;
           if( fluidPhaseId < numFluidPhases - 1 )
           {
-            globalIndex const compMassBalanceRow = totalMassBalanceRow + fluidPhaseId + 1; // component mass bal equations are shifted
+            globalIndex const compMassBalanceRow = totalMassBalanceRow + fluidPhaseId + 1;  // component mass bal equations are shifted
             localRhs[compMassBalanceRow] += rhsValue;
           }
         }
@@ -1124,8 +1361,6 @@ real64 ImmiscibleMultiphaseFlow::calculateResidualNorm( real64 const & GEOS_UNUS
   GEOS_LOG_LEVEL_RANK_0_NLR( logInfo::ResidualNorm, GEOS_FMT( "        ( R{} ) = ( {:4.2e} )",
                                                               coupledSolverAttributePrefix(), residualNorm ))
 
-  getConvergenceStats().setResidualValue( GEOS_FMT( "R{}", coupledSolverAttributePrefix()), residualNorm );
-
   return residualNorm;
 }
 
@@ -1158,7 +1393,7 @@ void ImmiscibleMultiphaseFlow::applySystemSolution( DofManager const & dofManage
                                                                 MeshLevel & mesh,
                                                                 string_array const & regionNames )
   {
-    stdVector< string > fields{ fields::flow::pressure::key(), fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() };
+    std::vector< string > fields{ fields::flow::pressure::key(), fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() };
 
     FieldIdentifiers fieldsToBeSync;
     fieldsToBeSync.addElementFields( fields, regionNames );
@@ -1176,6 +1411,7 @@ void ImmiscibleMultiphaseFlow::updateVolumeConstraint( ElementSubRegionBase & su
 
   forAll< parallelDevicePolicy<> >( subRegion.size(), [=] GEOS_HOST_DEVICE ( localIndex const ei )
   {
+    phaseVolumeFraction[ei][0] = fmin( 1.0, fmax( phaseVolumeFraction[ei][0], 0.0 ));;
     phaseVolumeFraction[ei][1] = 1.0 - phaseVolumeFraction[ei][0];
   } );
 }
@@ -1254,11 +1490,11 @@ void ImmiscibleMultiphaseFlow::implicitStepComplete( real64 const & time,
       CoupledSolidBase const & porousMaterial = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
       if( m_keepVariablesConstantDuringInitStep )
       {
-        porousMaterial.ignoreConvergedState(); // newPorosity <- porosity_n
+        porousMaterial.ignoreConvergedState();  // newPorosity <- porosity_n
       }
       else
       {
-        porousMaterial.saveConvergedState(); // porosity_n <- porosity
+        porousMaterial.saveConvergedState();  // porosity_n <- porosity
       }
 
       // Step 4: save converged state for the relperm model to handle hysteresis
@@ -1287,7 +1523,6 @@ void ImmiscibleMultiphaseFlow::implicitStepComplete( real64 const & time,
       }
     } );
   } );
-
 }
 
 void ImmiscibleMultiphaseFlow::saveConvergedState( ElementSubRegionBase & subRegion ) const
@@ -1407,4 +1642,4 @@ real64 ImmiscibleMultiphaseFlow::setNextDtBasedOnStateChange( real64 const & cur
 
 REGISTER_CATALOG_ENTRY( PhysicsSolverBase, ImmiscibleMultiphaseFlow, string const &, Group * const )
 
-} // namespace geos
+}  // namespace geos
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.hpp b/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.hpp
index 7526130316c..b3769837600 100644
--- a/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.hpp
+++ b/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.hpp
@@ -27,6 +27,12 @@
 namespace geos
 {
 
+
+namespace constitutive
+{
+class ConstitutiveBase;
+} // namespace constitutive
+
 //START_SPHINX_INCLUDE_00
 /**
  * @class ImmiscibleMultiphaseFlow
@@ -160,12 +166,11 @@ class ImmiscibleMultiphaseFlow : public FlowSolverBase
    * @param matrix the system matrix
    * @param rhs the system right-hand side vector
    */
-  virtual void
-  assembleFluxTerms( real64 const dt,
-                     DomainPartition const & domain,
-                     DofManager const & dofManager,
-                     CRSMatrixView< real64, globalIndex const > const & localMatrix,
-                     arrayView1d< real64 > const & localRhs ) const;
+  void assembleFluxTerms( real64 const dt,
+                          DomainPartition & domain,
+                          DofManager const & dofManager,
+                          CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                          arrayView1d< real64 > const & localRhs ) const;
 
   /**
    * @brief Function to perform the Application of Dirichlet type BC's
@@ -215,6 +220,10 @@ class ImmiscibleMultiphaseFlow : public FlowSolverBase
   struct viewKeyStruct : public FlowSolverBase::viewKeyStruct
   {
     // inputs
+    static constexpr char const * capPressureNamesString() { return "capPressureNames"; }
+    static constexpr char const * relPermNamesString() { return "relPermNames"; }
+    static constexpr char const * elemDofFieldString() { return "elemDofField"; }
+    static constexpr char const * interfaceFaceSetNamesString() { return "interfaceFaceSetNames"; }
 
     // density averaging scheme
     static constexpr char const * gravityDensitySchemeString()    { return "gravityDensityScheme"; }
@@ -228,9 +237,9 @@ class ImmiscibleMultiphaseFlow : public FlowSolverBase
     static constexpr char const * maxRelativePresChangeString() { return "maxRelativePressureChange"; }
     static constexpr char const * useTotalMassEquationString() { return "useTotalMassEquation"; }
 
-    static constexpr char const * capPressureNamesString() { return "capillary_pressure"; }
-    static constexpr char const * relPermNamesString() { return "relative_permeability"; }
-    static constexpr char const * elemDofFieldString() { return "elemDofField"; }
+//    static constexpr char const * capPressureNamesString() { return "capillary_pressure"; }
+//    static constexpr char const * relPermNamesString() { return "relative_permeability"; }
+//    static constexpr char const * elemDofFieldString() { return "elemDofField"; }
   };
 
 
@@ -300,6 +309,15 @@ class ImmiscibleMultiphaseFlow : public FlowSolverBase
   /// damping factor for solution change targets
   real64 m_solutionChangeScalingFactor;
 
+  string_array m_interfaceFaceSetNames;
+
+  stdVector< std::array< std::tuple< constitutive::RelativePermeabilityBase *,
+                                     constitutive::CapillaryPressureBase *,
+                                     constitutive::TwoPhaseImmiscibleFluid * >, 2 > >  m_interfaceConstitutivePairs;
+
+  unordered_map< localIndex, localIndex >  m_interfaceRegionByConnector;
+  unordered_map< localIndex, localIndex >  m_connectorIndicesByInterfaceRegion;
+
 
 private:
 
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/CapillaryPressureUpdateKernel.hpp b/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/CapillaryPressureUpdateKernel.hpp
new file mode 100644
index 00000000000..2a02f536ea9
--- /dev/null
+++ b/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/CapillaryPressureUpdateKernel.hpp
@@ -0,0 +1,73 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 TotalEnergies
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+/**
+ * @file CapillaryPressureUpdateKernel.hpp
+ */
+
+#ifndef GEOS_PHYSICSSOLVERS_FLUIDFLOW_IMMISCIBLEMULTIPHASE_CAPILLARYPRESSUREUPDATEKERNEL_HPP
+#define GEOS_PHYSICSSOLVERS_FLUIDFLOW_IMMISCIBLEMULTIPHASE_CAPILLARYPRESSUREUPDATEKERNEL_HPP
+
+#include "common/DataTypes.hpp"
+#include "common/GEOS_RAJA_Interface.hpp"
+
+namespace geos
+{
+
+namespace immiscibleMultiphaseKernels
+{
+
+/******************************** CapillaryPressureUpdateKernel ********************************/
+
+struct CapillaryPressureUpdateKernel
+{
+  template< typename POLICY, typename CAPPRES_WRAPPER >
+  static void
+  launch( localIndex const size,
+          CAPPRES_WRAPPER const & capPresWrapper,
+          arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const & phaseVolFrac )
+  {
+    forAll< POLICY >( size, [=] GEOS_HOST_DEVICE ( localIndex const k )
+    {
+      for( localIndex q = 0; q < capPresWrapper.numGauss(); ++q )
+      {
+        capPresWrapper.update( k, q, phaseVolFrac[k] );
+      }
+    } );
+  }
+
+  template< typename POLICY, typename CAPPRES_WRAPPER >
+  static void
+  launch( SortedArrayView< localIndex const > const & targetSet,
+          CAPPRES_WRAPPER const & capPresWrapper,
+          arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const & phaseVolFrac )
+  {
+    forAll< POLICY >( targetSet.size(), [=] GEOS_HOST_DEVICE ( localIndex const a )
+    {
+      localIndex const k = targetSet[a];
+      for( localIndex q = 0; q < capPresWrapper.numGauss(); ++q )
+      {
+        capPresWrapper.update( k, q, phaseVolFrac[k] );
+      }
+    } );
+  }
+};
+
+} // namespace immiscibleMultiphaseKernels
+
+} // namespace geos
+
+
+#endif //GEOS_PHYSICSSOLVERS_FLUIDFLOW_IMMISCIBLEMULTIPHASE_CAPILLARYPRESSUREUPDATEKERNEL_HPP
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp b/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp
index ebb78332b43..d1fdeb72625 100644
--- a/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp
+++ b/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp
@@ -17,39 +17,1311 @@
  * @file ImmiscibleMultiphaseKernels.hpp
  */
 
+
 #ifndef GEOS_PHYSICSSOLVERS_FLUIDFLOW_MULTIPHASEKERNELS_HPP
 #define GEOS_PHYSICSSOLVERS_FLUIDFLOW_MULTIPHASEKERNELS_HPP
 
-#include "codingUtilities/Utilities.hpp"
-#include "common/DataLayouts.hpp"
-#include "common/DataTypes.hpp"
-#include "common/GEOS_RAJA_Interface.hpp"
+
+ #include "codingUtilities/Utilities.hpp"
+ #include "common/DataLayouts.hpp"
+ #include "common/DataTypes.hpp"
+ #include "common/GEOS_RAJA_Interface.hpp"
+ #include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluid.hpp"
+ #include "constitutive/solid/CoupledSolidBase.hpp"
+ #include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluidFields.hpp"
+ #include "constitutive/capillaryPressure/CapillaryPressureFields.hpp"
+ #include "constitutive/capillaryPressure/CapillaryPressureBase.hpp"
+ #include "constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp"
+ #include "constitutive/capillaryPressure/TableCapillaryPressure.hpp"
+ #include "constitutive/permeability/PermeabilityBase.hpp"
+ #include "constitutive/permeability/PermeabilityFields.hpp"
+ #include "constitutive/relativePermeability/RelativePermeabilityBase.hpp"
+ #include "constitutive/relativePermeability/RelativePermeabilityFields.hpp"
+ #include "constitutive/ConstitutiveManager.hpp"
+#include "constitutive/capillaryPressure/CapillaryPressureSelector.hpp"
+#include "constitutive/relativePermeability/RelativePermeabilitySelector.hpp"
+
+#include "constitutive/ConstitutivePassThru.hpp"
 #include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluid.hpp"
-#include "constitutive/solid/CoupledSolidBase.hpp"
-#include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluidFields.hpp"
-#include "constitutive/capillaryPressure/CapillaryPressureFields.hpp"
-#include "constitutive/capillaryPressure/CapillaryPressureBase.hpp"
-#include "constitutive/permeability/PermeabilityBase.hpp"
-#include "constitutive/permeability/PermeabilityFields.hpp"
-#include "constitutive/relativePermeability/RelativePermeabilityBase.hpp"
-#include "constitutive/relativePermeability/RelativePermeabilityFields.hpp"
-#include "fieldSpecification/AquiferBoundaryCondition.hpp"
-#include "finiteVolume/BoundaryStencil.hpp"
-#include "finiteVolume/FluxApproximationBase.hpp"
-#include "linearAlgebra/interfaces/InterfaceTypes.hpp"
-#include "physicsSolvers/PhysicsSolverBaseKernels.hpp"
-#include "physicsSolvers/fluidFlow/FlowSolverBaseFields.hpp"
-#include "physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlowFields.hpp"
-#include "physicsSolvers/fluidFlow/CompositionalMultiphaseUtilities.hpp"
-#include "physicsSolvers/fluidFlow/StencilAccessors.hpp"
-#include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/KernelLaunchSelectors.hpp"
+
+
+ #include "fieldSpecification/AquiferBoundaryCondition.hpp"
+ #include "finiteVolume/BoundaryStencil.hpp"
+ #include "finiteVolume/CellElementStencilTPFA.hpp"
+ #include "finiteVolume/FluxApproximationBase.hpp"
+ #include "linearAlgebra/interfaces/InterfaceTypes.hpp"
+ #include "physicsSolvers/PhysicsSolverBaseKernels.hpp"
+ #include "physicsSolvers/fluidFlow/FlowSolverBaseFields.hpp"
+ #include "physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlowFields.hpp"
+ #include "physicsSolvers/fluidFlow/CompositionalMultiphaseUtilities.hpp"
+ #include "physicsSolvers/fluidFlow/StencilAccessors.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/compositional/RelativePermeabilityUpdateKernel.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/compositional/CapillaryPressureUpdateKernel.hpp"
+ #include "physicsSolvers/PhysicsSolverBaseKernels.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/KernelLaunchSelectors.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/KernelLaunchSelectors.hpp"
+
 
 namespace geos
 {
 namespace immiscibleMultiphaseKernels
 {
+
 using namespace constitutive;
 
+GEOS_HOST_DEVICE
+inline
+static void local_solver( real64 uT, stdVector< real64 > saturations, stdVector< real64 > pressures, stdVector< real64 > JFMultipliers, stdVector< real64 > trappedSats1,
+                          stdVector< real64 > trappedSats2, stdVector< real64 > transHat, stdVector< real64 > dTransHat_dP, stdVector< real64 > gravCoefHat, stdVector< real64 > gravCoef,
+                          stdVector< real64 >  cellCenterDuT, stdVector< real64 > cellCenterDens, stdVector< real64 > cellCenterDens_dP,
+                          std::vector< RelativePermeabilityBase * > relPerms, std::vector< CapillaryPressureBase * > capPressures,
+                          std::vector< TwoPhaseImmiscibleFluid * > fluids, std::vector< real64 > & phi, std::vector< real64 > & grad_phi_P, std::vector< real64 > & grad_phi_S, bool & converged )
+{
+
+  // getting wrappers:
+
+  constitutive::constitutiveUpdatePassThru( *capPressures[0], [&] ( auto & castedCapPres1 )
+  {
+    auto capPresWrapper1 = castedCapPres1.createKernelWrapper();
+
+
+    constitutive::constitutiveUpdatePassThru( *capPressures[1], [&] ( auto & castedCapPres2 )
+    {
+      auto capPresWrapper2 = castedCapPres2.createKernelWrapper();
+
+
+      constitutive::constitutiveUpdatePassThru( *relPerms[0], [&] ( auto & castedRelPerm1 )
+      {
+        auto relPermWrapper1 = castedRelPerm1.createKernelWrapper();
+
+
+        constitutive::constitutiveUpdatePassThru( *relPerms[1], [&] ( auto & castedRelPerm2 )
+        {
+          auto relPermWrapper2 = castedRelPerm2.createKernelWrapper();
+
+          auto fluidWrapper1 = fluids[0]->createKernelWrapper();
+          auto fluidWrapper2 = fluids[1]->createKernelWrapper();
+
+          // Create an output file stream object (ofstream) for analyzing the local solver's performance
+          std::ofstream outFile( "iterations2.csv" );
+
+
+          // Write data to the file
+          outFile << "Jacobian";
+          outFile << ",";
+          outFile << "residual";
+          outFile << ",";
+          outFile << "Fw_alpha";
+          outFile << ",";
+          outFile << "Fw_beta";
+          outFile << ",";
+          outFile << "Pc_int";
+          outFile << ",";
+          outFile << "Pc_int1";
+          outFile << ",";
+          outFile << "Pc_int2";
+          outFile << ",";
+          outFile << "Fn_alpha";
+          outFile << ",";
+          outFile << "Fn_beta";
+          outFile << ",";
+          outFile << "Vw_alpha";
+          outFile << ",";
+          outFile << "Vn_alpha";
+          outFile << ",";
+          outFile << "Vw_beta";
+          outFile << ",";
+          outFile << "Vn_beta";
+          outFile << ",";
+          outFile << "Gw_alpha";
+          outFile << ",";
+          outFile << "Gn_alpha";
+          outFile << ",";
+          outFile << "Gw_beta";
+          outFile << ",";
+          outFile << "Gn_beta";
+          outFile << ",";
+          outFile << "Cw_alpha";
+          outFile << ",";
+          outFile << "Cn_alpha";
+          outFile << ",";
+          outFile << "Cw_beta";
+          outFile << ",";
+          outFile << "Cn_beta";
+          outFile << ",";
+          outFile << "Pc1_ip0";
+          outFile << ",";
+          outFile << "Pc1_ip1";
+          outFile << ",";
+          outFile << "S_alpha";
+          outFile << ",";
+          outFile << "S_beta";
+          outFile << std::endl;
+
+          // nonlinear solver's parameters
+          real64 tol = 1.0e-9;
+          int max_iter = 50;
+          converged = 0;
+          bool damping = true;
+          bool bisection = false;
+          // bool lineSearch = false;
+          bool newton_path = false;
+
+          // Local newton loop:
+
+          // Use of the capillary pressure kernel wrapper
+
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseVolFrac1( 1, 2 );
+          StackArray< real64, 3, 2, constitutive::cappres::LAYOUT_CAPPRES > capPres1( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dPhaseVolFrac_dCapPres1( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dCapPres1_dPhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > facePhaseVolFrac1( 1, 2 );
+          StackArray< real64, 3, 2, constitutive::cappres::LAYOUT_CAPPRES > faceCapPres1( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dfacePhaseVolFrac_dCapPres1( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dCapPres1_dfacePhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseVolFrac2( 1, 2 );
+          StackArray< real64, 3, 2, constitutive::cappres::LAYOUT_CAPPRES > capPres2( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dPhaseVolFrac_dCapPres2( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dCapPres2_dPhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > facePhaseVolFrac2( 1, 2 );
+          StackArray< real64, 3, 2, constitutive::cappres::LAYOUT_CAPPRES > faceCapPres2( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dfacePhaseVolFrac_dCapPres2( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dCapPres2_dfacePhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 1, 2 > JFunc1( 2 );
+          StackArray< real64, 1, 2 > JFunc2( 2 );
+
+          phaseVolFrac1[0][0] = saturations[0];
+          phaseVolFrac1[0][1] = 1.0 - saturations[0];
+
+          phaseVolFrac2[0][0] = saturations[1];
+          phaseVolFrac2[0][1] = 1.0 - saturations[1];
+
+          real64 Pc1_min = 0.0;
+          real64 Pc2_min = 0.0;
+          real64 Pc1_max = 0.0;
+          real64 Pc2_max = 0.0;
+
+          real64 density2[2]{};
+          real64 dDens_dP2[2][2]{};
+
+          density2[0] =  cellCenterDens[0];
+          density2[1] =  cellCenterDens[1];
+
+          dDens_dP2[0][0] = cellCenterDens_dP[0];
+          dDens_dP2[0][1] = cellCenterDens_dP[1];
+          dDens_dP2[1][0] = cellCenterDens_dP[2];
+          dDens_dP2[1][1] = cellCenterDens_dP[3];
+
+          JFunc1[0] = JFMultipliers[0];
+          JFunc2[0] = JFMultipliers[1];
+
+          using T1 = std::decay_t< decltype(castedCapPres1) >;
+          if constexpr (std::is_same_v< T1, JFunctionCapillaryPressure >) {
+            capPresWrapper1.compute( phaseVolFrac1[0],
+                                     JFunc1.toSliceConst(),
+                                     capPres1[0][0],
+                                     dCapPres1_dPhaseVolFrac[0][0] );
+
+            facePhaseVolFrac1[0][1] = 0.0;
+            facePhaseVolFrac1[0][0] = 1.0;
+            capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                     JFunc1.toSliceConst(),
+                                     faceCapPres1[0][0],
+                                     dCapPres1_dfacePhaseVolFrac[0][0] );
+            Pc1_min = faceCapPres1[0][0][0];
+            facePhaseVolFrac1[0][1] = 1.0;
+            facePhaseVolFrac1[0][0] = 0.0;
+            capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                     JFunc1.toSliceConst(),
+                                     faceCapPres1[0][0],
+                                     dCapPres1_dfacePhaseVolFrac[0][0] );
+            Pc1_max = faceCapPres1[0][0][0];
+
+          }
+          else
+          {
+            capPresWrapper1.compute( phaseVolFrac1[0],
+                                     capPres1[0][0],
+                                     dCapPres1_dPhaseVolFrac[0][0] );
+
+            facePhaseVolFrac1[0][1] = 0.0;
+            facePhaseVolFrac1[0][0] = 1.0;
+            capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                     faceCapPres1[0][0],
+                                     dCapPres1_dfacePhaseVolFrac[0][0] );
+            Pc1_min = faceCapPres1[0][0][0];
+            facePhaseVolFrac1[0][1] = 1.0;
+            facePhaseVolFrac1[0][0] = 0.0;
+            capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                     faceCapPres1[0][0],
+                                     dCapPres1_dfacePhaseVolFrac[0][0] );
+            Pc1_max = faceCapPres1[0][0][0];
+          }
+
+          using T2 = std::decay_t< decltype(castedCapPres2) >;
+          if constexpr (std::is_same_v< T2, JFunctionCapillaryPressure >) {
+            // evaluating cell-center Pc:
+
+            capPresWrapper2.compute( phaseVolFrac2[0],
+                                     JFunc2.toSliceConst(),
+                                     capPres2[0][0],
+                                     dCapPres2_dPhaseVolFrac[0][0] );
+
+// finding endpoints:
+
+            facePhaseVolFrac2[0][1] = 0.0;
+            facePhaseVolFrac2[0][0] = 1.0;
+            capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                     JFunc2.toSliceConst(),
+                                     faceCapPres2[0][0],
+                                     dCapPres2_dfacePhaseVolFrac[0][0] );
+            Pc2_min = faceCapPres2[0][0][0];
+            facePhaseVolFrac2[0][1] = 1.0;
+            facePhaseVolFrac2[0][0] = 0.0;
+            capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                     JFunc2.toSliceConst(),
+                                     faceCapPres2[0][0],
+                                     dCapPres2_dfacePhaseVolFrac[0][0] );
+            Pc2_max = faceCapPres2[0][0][0];
+
+          }
+          else
+          {
+            // evaluating cell-center Pc:
+
+            capPresWrapper2.compute( phaseVolFrac2[0],
+                                     capPres2[0][0],
+                                     dCapPres2_dPhaseVolFrac[0][0] );
+
+// finding endpoints:
+
+            facePhaseVolFrac2[0][1] = 0.0;
+            facePhaseVolFrac2[0][0] = 1.0;
+            capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                     faceCapPres2[0][0],
+                                     dCapPres2_dfacePhaseVolFrac[0][0] );
+            Pc2_min = faceCapPres2[0][0][0];
+            facePhaseVolFrac2[0][1] = 1.0;
+            facePhaseVolFrac2[0][0] = 0.0;
+            capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                     faceCapPres2[0][0],
+                                     dCapPres2_dfacePhaseVolFrac[0][0] );
+            Pc2_max = faceCapPres2[0][0][0];
+          }
+
+          // Use of the relative permeability kernel wrapper
+
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > faceTrappedVolFrac1( 1, 1, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > faceRelPerm1( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::relperm::LAYOUT_RELPERM_DS > dfacePhaseRelPerm1_dPhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > trappedVolFrac1( 1, 1, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > relPerm1( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::relperm::LAYOUT_RELPERM_DS > dPhaseRelPerm1_dPhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > faceTrappedVolFrac2( 1, 1, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > faceRelPerm2( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::relperm::LAYOUT_RELPERM_DS > dfacePhaseRelPerm2_dPhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > trappedVolFrac2( 1, 1, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > relPerm2( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::relperm::LAYOUT_RELPERM_DS > dPhaseRelPerm2_dPhaseVolFrac( 1, 1, 2, 2 );
+
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseMaxHistoricalVolFraction1( 1, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseMinHistoricalVolFraction1( 1, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseMaxHistoricalVolFraction2( 1, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseMinHistoricalVolFraction2( 1, 2 );
+
+          // compute relative permeability for both cell centers:
+
+          trappedVolFrac1[0][0][0] = trappedSats1[0];
+          trappedVolFrac1[0][0][1] = trappedSats1[1];
+
+          trappedVolFrac2[0][0][0] = trappedSats2[0];
+          trappedVolFrac2[0][0][1] = trappedSats2[1];
+
+          faceTrappedVolFrac1[0][0][0] = trappedSats1[0];
+          faceTrappedVolFrac1[0][0][1] = trappedSats1[1];
+
+          faceTrappedVolFrac2[0][0][0] = trappedSats2[0];
+          faceTrappedVolFrac2[0][0][1] = trappedSats2[1];
+
+          using T5 = std::decay_t< decltype(castedRelPerm1) >;
+          if constexpr (std::is_same_v< T5, constitutive::TableRelativePermeabilityHysteresis >) {
+            relPermWrapper1.compute( phaseVolFrac1[0],
+                                     phaseMaxHistoricalVolFraction1[0],
+                                     phaseMinHistoricalVolFraction1[0],
+                                     trappedVolFrac1[0][0],
+                                     relPerm1[0][0],
+                                     dPhaseRelPerm1_dPhaseVolFrac[0][0] );
+
+          }
+          else
+          {
+
+            relPermWrapper1.compute( phaseVolFrac1[0],
+                                     trappedVolFrac1[0][0],
+                                     relPerm1[0][0],
+                                     dPhaseRelPerm1_dPhaseVolFrac[0][0] );
+          }
+
+          using T6 = std::decay_t< decltype(castedRelPerm2) >;
+          if constexpr (std::is_same_v< T6, constitutive::TableRelativePermeabilityHysteresis >) {
+            relPermWrapper2.compute( phaseVolFrac2[0],
+                                     phaseMaxHistoricalVolFraction2[0],
+                                     phaseMinHistoricalVolFraction2[0],
+                                     trappedVolFrac2[0][0],
+                                     relPerm2[0][0],
+                                     dPhaseRelPerm2_dPhaseVolFrac[0][0] );
+
+          }
+          else
+          {
+
+            relPermWrapper2.compute( phaseVolFrac2[0],
+                                     trappedVolFrac2[0][0],
+                                     relPerm2[0][0],
+                                     dPhaseRelPerm2_dPhaseVolFrac[0][0] );
+          }
+
+
+          // Use of the fluid model kernel wrapper
+          StackArray< real64, 3, 2, constitutive::multifluid::LAYOUT_PHASE > phaseDensity1( 1, 1, 2 );
+          StackArray< real64, 3, 2, constitutive::multifluid::LAYOUT_PHASE > phaseViscosity1( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::multifluid::LAYOUT_PHASE_DC > dPhaseDens1_dP( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::multifluid::LAYOUT_PHASE_DC > dPhaseVisc1_dP( 1, 1, 2, 2 );
+          StackArray< real64, 3, 2, constitutive::multifluid::LAYOUT_PHASE > phaseDensity2( 1, 1, 2 );
+          StackArray< real64, 3, 2, constitutive::multifluid::LAYOUT_PHASE > phaseViscosity2( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::multifluid::LAYOUT_PHASE_DC > dPhaseDens2_dP( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::multifluid::LAYOUT_PHASE_DC > dPhaseVisc2_dP( 1, 1, 2, 2 );
+
+          // Declare the MultiFluidVar (PhaseProp) type
+          TwoPhaseImmiscibleFluid::PhaseProp phaseDensity_temp1;
+          TwoPhaseImmiscibleFluid::PhaseProp phaseViscosity_temp1;
+          phaseDensity_temp1.value.resize( 1, 1, 2 ); // or whatever sizes you need
+          phaseDensity_temp1.derivs.resize( 1, 1, 2, 2 ); // make sure all dims > 0
+          phaseViscosity_temp1.value.resize( 1, 1, 2 ); // or whatever sizes you need
+          phaseViscosity_temp1.derivs.resize( 1, 1, 2, 2 ); // make sure all dims > 0
+
+          auto phaseDensitySlice0 = TwoPhaseImmiscibleFluid::PhaseProp::SliceType(
+            phaseDensity_temp1.value[0][0], phaseDensity_temp1.derivs[0][0] );
+          auto phaseViscositySlice0 = TwoPhaseImmiscibleFluid::PhaseProp::SliceType(
+            phaseViscosity_temp1.value[0][0], phaseViscosity_temp1.derivs[0][0] );
+          fluidWrapper1.compute( pressures[0], phaseDensitySlice0, phaseViscositySlice0 );
+
+          // Temporary:
+          phaseDensity1[0][0][0] = phaseDensitySlice0.value[0];
+          phaseDensity1[0][0][1] = phaseDensitySlice0.value[1];
+          dPhaseDens1_dP[0][0][0][0] = phaseDensitySlice0.derivs[0][0];
+          dPhaseDens1_dP[0][0][0][1] = 0;
+          dPhaseDens1_dP[0][0][1][0] = phaseDensitySlice0.derivs[1][0];
+          dPhaseDens1_dP[0][0][1][1] = 0;
+
+          phaseViscosity1[0][0][0] = phaseViscositySlice0.value[0];
+          phaseViscosity1[0][0][1] = phaseViscositySlice0.value[1];
+          dPhaseVisc1_dP[0][0][0][0] = phaseViscositySlice0.derivs[0][0];
+          dPhaseVisc1_dP[0][0][0][1] = 0;
+          dPhaseVisc1_dP[0][0][1][0] = phaseViscositySlice0.derivs[1][0];
+          dPhaseVisc1_dP[0][0][1][1] = 0;
+
+          auto phaseDensitySlice1 = TwoPhaseImmiscibleFluid::PhaseProp::SliceType(
+            phaseDensity_temp1.value[0][0], phaseDensity_temp1.derivs[0][0] );
+          auto phaseViscositySlice1 = TwoPhaseImmiscibleFluid::PhaseProp::SliceType(
+            phaseViscosity_temp1.value[0][0], phaseViscosity_temp1.derivs[0][0] );
+          fluidWrapper2.compute( pressures[1], phaseDensitySlice1, phaseViscositySlice1 );
+
+
+          phaseDensity2[0][0][0] = phaseDensitySlice1.value[0];
+          phaseDensity2[0][0][1] = phaseDensitySlice1.value[1];
+          dPhaseDens2_dP[0][0][0][0] = phaseDensitySlice1.derivs[0][0];
+          dPhaseDens2_dP[0][0][0][1] = 0;
+          dPhaseDens2_dP[0][0][1][0] = phaseDensitySlice1.derivs[1][0];
+          dPhaseDens2_dP[0][0][1][1] = 0;
+
+          phaseViscosity2[0][0][0] = phaseViscositySlice1.value[0];
+          phaseViscosity2[0][0][1] = phaseViscositySlice1.value[1];
+          dPhaseVisc2_dP[0][0][0][0] = phaseViscositySlice1.derivs[0][0];
+          dPhaseVisc2_dP[0][0][0][1] = 0;
+          dPhaseVisc2_dP[0][0][1][0] = phaseViscositySlice1.derivs[1][0];
+          dPhaseVisc2_dP[0][0][1][1] = 0;
+
+          // clear working arrays
+          real64 halfFluxVal[2][2]{};
+          real64 dhalfFlux1_dP[2][2]{};
+          real64 dhalfFlux1_dS[2][2]{};
+          real64 dhalfFlux2_dP[2][2]{};
+          real64 dhalfFlux2_dS[2][2]{};
+          real64 dhalfFlux_duT[2][2]{};
+          real64 dhalfFlux_dpc[2][2]{};
+
+          //new
+          real64 fluxVal[2]{};
+          real64 dFlux_dP[2][2]{};
+          real64 dFlux_dS[2][2]{};
+
+          real64 duT_dP[2]{};
+          real64 duT_dS[2]{};
+
+          duT_dP[0] = cellCenterDuT[0];
+          duT_dP[1] = cellCenterDuT[1];
+
+          duT_dS[0] = cellCenterDuT[2];
+          duT_dS[1] = cellCenterDuT[3];
+
+          // initial guess:
+
+          real64 const Pc1 = capPres1[0][0][0];
+          real64 const Pc2 = capPres2[0][0][0];
+
+          real64 Pc_int = ( Pc1 + Pc2 ) / 2.0;
+
+          real64 Pc_min_all = fmax( Pc1_min, Pc2_min );
+          real64 Pc_max_all = fmin( Pc1_max, Pc2_max );
+
+          if( Pc_int < Pc_min_all || Pc_int > Pc_max_all )
+          {
+            Pc_int = ( Pc_min_all + Pc_max_all ) / 2.0;
+          }
+
+          // While loop (newton loop)
+          int iter = 0;
+          int div = 0;
+          // int ext_iter0 = 0;
+          // int ext_iter1 = 0;
+          real64 next_Pc_int = 0.0;
+          real64 old_Pc_int = 0.0;
+          real64 old_residual = 0.0;
+
+          if( bisection )
+          {
+            Pc_int = fmax( Pc1_max, Pc2_max );
+            next_Pc_int = fmin( Pc1_min, Pc2_min );
+          }
+
+          if( newton_path )
+          {
+            Pc_int = fmax( Pc1_max, Pc2_max );
+            Pc_int = 2.0e5;
+            next_Pc_int = (fmax( Pc1_max, Pc2_max ) - fmin( Pc1_min, Pc2_min )) / (max_iter - 1);
+            next_Pc_int = (2.0e5 - 5.0e4) / (max_iter - 1);
+          }
+
+          real64 Pc_int_iterate = Pc_int;
+
+          while( iter < max_iter )
+          {
+
+            Pc_int_iterate = Pc_int;
+
+            // clear working arrays
+            real64 density[2]{};
+            real64 dDens_dP[2][2]{};
+            real64 gravityCof[2]{};
+            real64 viscosity[2]{};
+            real64 dVisc_dP[2][2]{};
+
+            real64 viscous[2][2]{};
+            real64 bouyancy[2][2]{};
+            real64 capillarity[2][2]{};
+
+            real64 dV1_dS[2][2]{};
+            real64 dG1_dS[2][2]{};
+            real64 dC1_dS[2][2]{};
+            real64 dV2_dS[2][2]{};
+            real64 dG2_dS[2][2]{};
+            real64 dC2_dS[2][2]{};
+            real64 dV1_dpc[2][2]{};
+            real64 dG1_dpc[2][2]{};
+            real64 dC1_dpc[2][2]{};
+            real64 dV2_dpc[2][2]{};
+            real64 dG2_dpc[2][2]{};
+            real64 dC2_dpc[2][2]{};
+
+            real64 local_residual = 0;
+            real64 local_jacobian = 0;
+
+            // truncate the capillary pressure iterate (ensures the inverse will compute a saturation bounded between 0 and 1):
+
+            Pc_int = fmin( fmax( Pc1_max, Pc2_max ), fmax( Pc_int, fmin( Pc1_min, Pc2_min ) ));
+
+            faceCapPres1[0][0][0] = fmin( Pc1_max, fmax( Pc_int, Pc1_min ));
+            faceCapPres2[0][0][0] = fmin( Pc2_max, fmax( Pc_int, Pc2_min ));
+
+            // Compute the inverse:
+
+            JFunc1[0] = JFMultipliers[0];
+            JFunc2[0] = JFMultipliers[1];
+
+            using T3 = std::decay_t< decltype(castedCapPres1) >;
+            if constexpr (std::is_same_v< T3, JFunctionCapillaryPressure >) {
+              capPresWrapper1.computeInv( facePhaseVolFrac1[0],
+                                          JFunc1.toSliceConst(),
+                                          faceCapPres1[0][0],
+                                          dfacePhaseVolFrac_dCapPres1[0][0] );
+              facePhaseVolFrac1[0][0] = fmin( 1.0, fmax( facePhaseVolFrac1[0][0], 0.0 ));
+              facePhaseVolFrac1[0][1] = fmin( 1.0, fmax( facePhaseVolFrac1[0][1], 0.0 ));
+              //get derivatives:
+              capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                       JFunc1.toSliceConst(),
+                                       faceCapPres1[0][0],
+                                       dCapPres1_dfacePhaseVolFrac[0][0] );
+
+            }
+            else
+            {
+              capPresWrapper1.computeInv( facePhaseVolFrac1[0],
+                                          faceCapPres1[0][0],
+                                          dfacePhaseVolFrac_dCapPres1[0][0] );
+              facePhaseVolFrac1[0][0] = fmin( 1.0, fmax( facePhaseVolFrac1[0][0], 0.0 ));
+              facePhaseVolFrac1[0][1] = fmin( 1.0, fmax( facePhaseVolFrac1[0][1], 0.0 ));
+              //get derivatives:
+              capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                       faceCapPres1[0][0],
+                                       dCapPres1_dfacePhaseVolFrac[0][0] );
+            }
+
+            using T4 = std::decay_t< decltype(castedCapPres2) >;
+            if constexpr (std::is_same_v< T4, JFunctionCapillaryPressure >) {
+              // evaluating cell-center Pc:
+              capPresWrapper2.computeInv( facePhaseVolFrac2[0],
+                                          JFunc2.toSliceConst(),
+                                          faceCapPres2[0][0],
+                                          dfacePhaseVolFrac_dCapPres2[0][0] );
+              facePhaseVolFrac2[0][0] = fmin( 1.0, fmax( facePhaseVolFrac2[0][0], 0.0 ));
+              facePhaseVolFrac2[0][1] = fmin( 1.0, fmax( facePhaseVolFrac2[0][1], 0.0 ));
+
+//get derivatives:
+
+              capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                       JFunc2.toSliceConst(),
+                                       faceCapPres2[0][0],
+                                       dCapPres2_dfacePhaseVolFrac[0][0] );
+
+            }
+            else
+            {
+              // evaluating cell-center Pc:
+              capPresWrapper2.computeInv( facePhaseVolFrac2[0],
+                                          faceCapPres2[0][0],
+                                          dfacePhaseVolFrac_dCapPres2[0][0] );
+              facePhaseVolFrac2[0][0] = fmin( 1.0, fmax( facePhaseVolFrac2[0][0], 0.0 ));
+              facePhaseVolFrac2[0][1] = fmin( 1.0, fmax( facePhaseVolFrac2[0][1], 0.0 ));
+
+//get derivatives:
+
+              capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                       faceCapPres2[0][0],
+                                       dCapPres2_dfacePhaseVolFrac[0][0] );
+            }
+
+            // compute relative permeability for both faces:
+
+            using T7 = std::decay_t< decltype(castedRelPerm1) >;
+            if constexpr (std::is_same_v< T7, constitutive::TableRelativePermeabilityHysteresis >) {
+
+              relPermWrapper1.compute( facePhaseVolFrac1[0],
+                                       phaseMaxHistoricalVolFraction1[0],
+                                       phaseMinHistoricalVolFraction1[0],
+                                       faceTrappedVolFrac1[0][0],
+                                       faceRelPerm1[0][0],
+                                       dfacePhaseRelPerm1_dPhaseVolFrac[0][0] );
+
+            }
+            else
+            {
+
+              relPermWrapper1.compute( facePhaseVolFrac1[0],
+                                       faceTrappedVolFrac1[0][0],
+                                       faceRelPerm1[0][0],
+                                       dfacePhaseRelPerm1_dPhaseVolFrac[0][0] );
+            }
+
+            using T8 = std::decay_t< decltype(castedRelPerm2) >;
+            if constexpr (std::is_same_v< T8, constitutive::TableRelativePermeabilityHysteresis >) {
+
+              relPermWrapper2.compute( facePhaseVolFrac2[0],
+                                       phaseMaxHistoricalVolFraction2[0],
+                                       phaseMinHistoricalVolFraction2[0],
+                                       faceTrappedVolFrac2[0][0],
+                                       faceRelPerm2[0][0],
+                                       dfacePhaseRelPerm2_dPhaseVolFrac[0][0] );
+
+            }
+            else
+            {
+
+              relPermWrapper2.compute( facePhaseVolFrac2[0],
+                                       faceTrappedVolFrac2[0][0],
+                                       faceRelPerm2[0][0],
+                                       dfacePhaseRelPerm2_dPhaseVolFrac[0][0] );
+            }
+
+
+            // Brenier and Jaffre's PPU upwinding:
+            bool check = false;
+            bool k_up_0_w = 1;
+            bool k_up_1_w = 1;
+            bool k_up_0_n = 1;
+            bool k_up_1_n = 1;
+
+            if( uT < 0.0 )
+            {
+              k_up_0_w = 0;
+              k_up_1_w = 0;
+              k_up_0_n = 0;
+              k_up_1_n = 0;
+            }
+
+            if( std::fabs( uT ) < 1e-20 )
+            {
+              k_up_0_w = 1;
+              k_up_1_w = 1;
+              k_up_0_n = 0;
+              k_up_1_n = 0;
+            }
+
+
+            localIndex k_up_0[2] = {static_cast< localIndex >(!k_up_0_w), static_cast< localIndex >(!k_up_0_n)};
+            localIndex k_up_1[2] = {static_cast< localIndex >(k_up_1_w), static_cast< localIndex >(k_up_1_n)};
+            bool k_up_0_check[2] = {false, false};
+            bool k_up_1_check[2] = {false, false};
+
+            while( !check )
+            {
+              k_up_0_check[0] = false;
+              k_up_0_check[1] = false;
+              k_up_1_check[0] = false;
+              k_up_1_check[1] = false;
+              for( integer ix = 0; ix < 2; ++ix ) // for loop over each half flux
+              {
+
+                // clear working arrays for each half flux:
+                real64 densMean[2]{};
+                real64 dDensMean_dP[2][2]{};
+
+                real64 presGrad[2]{};
+                real64 dPresGrad_dP[2][2]{};
+
+                real64 gravHead[2]{};
+                real64 dGravHead_dP[2][2]{};
+
+                real64 capGrad[2]{};
+                // real64 capPresIC[2][2]{};
+                // real64 jFMultiplier[2][2]{};
+                real64 dCapGrad_dP[2][2]{};
+                real64 dCapGrad_dS[2][2]{};
+
+                real64 mobility[2]{};
+                real64 dMob_dP[2][2]{};
+                real64 dMob_dS[2][2]{};
+
+                real64 total_mobility = 0;
+                gravityCof[0] = 0;
+                gravityCof[1] = 0;
+
+                for( integer ip = 0; ip < 2; ++ip ) // loop over phases
+                {
+                  // calculate quantities on primary connected cells
+                  if( ix == 0 )
+                  {
+                    density[ip]  = phaseDensity1[0][0][ip];
+                    dDens_dP[ip][ix] = dPhaseDens1_dP[0][0][ip][ip];
+
+                    viscosity[ip]  = phaseViscosity1[0][0][ip];
+                    dVisc_dP[ip][ix] = dPhaseVisc1_dP[0][0][ip][ip];
+                  }
+                  else
+                  {
+                    density[ip]  = phaseDensity2[0][0][ip];
+                    dDens_dP[ip][ix] = dPhaseDens2_dP[0][0][ip][ip];
+
+                    viscosity[ip]  = phaseViscosity2[0][0][ip];
+                    dVisc_dP[ip][ix] = dPhaseVisc2_dP[0][0][ip][ip];
+                  }
+
+                  densMean[ip] = density[ip];
+                  dDensMean_dP[ip][0] = dDens_dP[ip][ix];
+                  dDensMean_dP[ip][1] = dDens_dP[ip][ix];
+
+                  //***** calculation of flux *****
+
+                  // compute potential difference
+                  real64 potScale = 0.0;
+                  real64 dPresGrad_dTrans = 0.0;
+                  real64 dGravHead_dTrans = 0.0;
+                  real64 dCapGrad_dTrans = 0.0;
+                  constexpr int signPotDiff[2] = {1, -1};
+                  constexpr int signTix[2] = {1, -1};
+
+                  for( integer ke = 0; ke < 2; ++ke )
+                  {
+
+                    real64 const pressure = pressures[ix];
+                    presGrad[ip] += signTix[ke] * transHat[ix] * pressure;
+                    dPresGrad_dTrans += signPotDiff[ke] * pressure;
+                    dPresGrad_dP[ip][ke] = signTix[ke] * transHat[ix];
+
+                    real64 gravD = 0.0;
+
+                    if( ke == 0 )
+                    {
+                      gravD += signTix[ke] * transHat[ix] * gravCoef[ix];
+                    }
+                    else
+                    {
+                      gravD += signTix[ke] * transHat[ix] * gravCoefHat[ix];
+                    }
+
+                    real64 pot = signTix[ke] * transHat[ix] * pressure - densMean[ip] * gravD;
+
+                    gravHead[ip] += densMean[ip] * gravD;
+                    gravityCof[ip] += gravD;
+
+                    dGravHead_dTrans += signPotDiff[ke] * densMean[ip] * gravCoefHat[ix];
+
+                    for( integer i = 0; i < 2; ++i )
+                    {
+                      dGravHead_dP[ip][i] += dDensMean_dP[ip][i] * gravD;
+                    }
+
+                    real64 capPres = capPres1[0][0][ip];
+
+                    if( ke == 1 && ix == 0 )
+                    {
+                      capPres = faceCapPres1[0][0][ip];
+                    }
+                    else if( ke == 1 && ix == 1 )
+                    {
+                      capPres = faceCapPres2[0][0][ip];
+                    }
+                    else if( ke == 0 && ix == 1 )
+                    {
+
+                      capPres = capPres2[0][0][ip];
+                    }
+
+                    dCapGrad_dTrans -= signPotDiff[ke] * capPres;
+                    pot -= signTix[ke] * transHat[ix] * capPres;
+
+                    capGrad[ip] -= signTix[ke] * transHat[ix] * capPres;
+
+                    potScale = fmax( potScale, fabs( pot ) );
+                  }
+
+                  for( integer ke = 0; ke < 2; ++ke )
+                  {
+                    dPresGrad_dP[ip][ke] += signTix[ke] * dTransHat_dP[ix] * dPresGrad_dTrans;
+
+                    dGravHead_dP[ip][ke] += signTix[ke] * dTransHat_dP[ix] * dGravHead_dTrans;
+
+                    // real64 constexpr eps = 1e-18;
+                    real64 dCapPres_dS = dCapPres1_dPhaseVolFrac[0][0][ip][ip];
+
+                    if( ke == 1 && ix == 0 )
+                    {
+                      dCapPres_dS = dCapPres1_dfacePhaseVolFrac[0][0][ip][ip];
+                    }
+                    else if( ke == 1 && ix == 1 )
+                    {
+                      dCapPres_dS = dCapPres2_dfacePhaseVolFrac[0][0][ip][ip];
+                    }
+                    else if( ke == 0 && ix == 1 )
+                    {
+                      dCapPres_dS = dCapPres2_dPhaseVolFrac[0][0][ip][ip];
+                    }
+
+                    dCapGrad_dP[ip][ke] += signTix[ke] * dTransHat_dP[ix] * dCapGrad_dTrans;
+                    dCapGrad_dS[ip][ke] -= signTix[ke] * transHat[ix] * dCapPres_dS;
+                  }
+
+                  // *** upwinding ***
+                  // compute potential gradient
+//                  real64 potGrad = presGrad[ip] - gravHead[ip];
+
+//                  potGrad += capGrad[ip];
+
+                  // choose upstream cell
+                  constexpr int sign[2] = {1, -1};
+
+                  if( k_up_0[ip] == 1 && ix == 0 )
+                  {
+                    mobility[ip] = faceRelPerm1[0][0][ip] / viscosity[ip];
+                    dMob_dP[ip][k_up_0[ip]] = mobility[ip] * (-dVisc_dP[ip][ix] / viscosity[ip]);
+
+                    dMob_dS[ip][k_up_0[ip]] = sign[ip] * dfacePhaseRelPerm1_dPhaseVolFrac[0][0][ip][ip] / viscosity[ip];
+                  }
+                  else if( k_up_1[ip] == 0 && ix == 1 )
+                  {
+                    mobility[ip] = relPerm2[0][0][ip] / viscosity[ip];
+                    dMob_dP[ip][0] = mobility[ip] * (-dVisc_dP[ip][ix] / viscosity[ip]);
+                    dMob_dS[ip][0] = sign[ip] * dPhaseRelPerm2_dPhaseVolFrac[0][0][ip][ip] / viscosity[ip];
+                  }
+                  else if( k_up_1[ip] == 1 && ix == 1 )
+                  {
+                    mobility[ip] = faceRelPerm2[0][0][ip] / viscosity[ip];
+                    dMob_dP[ip][1] = mobility[ip] * (-dVisc_dP[ip][ix] / viscosity[ip]);
+                    dMob_dS[ip][1] = sign[ip] * dfacePhaseRelPerm2_dPhaseVolFrac[0][0][ip][ip] / viscosity[ip];
+                  }
+                  else
+                  {
+                    mobility[ip] = relPerm1[0][0][ip] / viscosity[ip];
+                    dMob_dP[ip][ix] = mobility[ip] * (-dVisc_dP[ip][ix] / viscosity[ip]);
+                    dMob_dS[ip][ix] = sign[ip] * dPhaseRelPerm1_dPhaseVolFrac[0][0][ip][ip] / viscosity[ip];
+                  }
+                  real64 constexpr eps = 0.0;
+                  total_mobility += mobility[ip] + eps;
+                } // loop over phases
+
+                /// Three Forces Flux Contribution: 1- Viscous 2- Gravitational 3- Capillary
+                constexpr int sign[2] = {1, -1};
+                // real64 constexpr eps = 0.0;
+
+                // loop over phases
+                for( integer ip = 0; ip < 2; ++ip )
+                {
+                  // 1- Viscous: pressure gradient depends on all points in the stencil
+                  viscous[ip][ix] = mobility[ip] / total_mobility * uT;
+                  halfFluxVal[ip][ix] = viscous[ip][ix];
+
+                  for( integer ke = 0; ke < 2; ++ke )
+                  {
+                    real64 dV_dP = sign[ip] * (dMob_dP[0][ke] * mobility[1] - dMob_dP[1][ke] * mobility[0]) / (total_mobility * total_mobility) * uT;
+                    real64 dV_dS = sign[ip] * (dMob_dS[0][ke] * mobility[1] - dMob_dS[1][ke] * mobility[0]) / (total_mobility * total_mobility) * uT;
+                    real64 dV_du = mobility[ip] / total_mobility;
+
+                    if( ix == 0 )
+                    {
+                      dV1_dS[ip][ke] = dV_dS;
+                      dhalfFlux1_dP[ip][ke] = dV_dP;
+                      dhalfFlux1_dS[ip][ke] = dV1_dS[ip][ke];
+                      dhalfFlux_duT[ip][ix] = dV_du;
+                      dV1_dpc[ip][ke] = dV1_dS[ip][ke] * dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+                      // GEOS_UNUSED_VAR( dV1_dpc[ip][ke] );
+                      GEOS_UNUSED_VAR( dhalfFlux_duT[ip][ix] );
+                    }
+                    else
+                    {
+                      dV2_dS[ip][ke] = dV_dS;
+                      dhalfFlux2_dP[ip][ke] =  dV_dP;
+                      dhalfFlux2_dS[ip][ke] =  dV2_dS[ip][ke];
+                      dhalfFlux_duT[ip][ix]= dV_du;
+                      dV2_dpc[ip][ke] = dV2_dS[ip][ke] * dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+                      // GEOS_UNUSED_VAR( dV2_dpc[ip][ke] );
+                      GEOS_UNUSED_VAR( dhalfFlux_duT[ip][ix] );
+                    }
+                  }
+
+                  // 2- Gravitational: gravitational head depends only on the two cells connected (same as mean density)
+                  bouyancy[ip][ix] = -1.0 * sign[ix] * sign[ip] * mobility[0] * mobility[1] / total_mobility * gravityCof[0] * (density[0] - density[1]);
+                  halfFluxVal[ip][ix] += bouyancy[ip][ix];
+
+                  for( integer ke = 0; ke < 2; ++ke )
+                  {
+                    real64 dG_dP = sign[ix] * sign[ip] * (dMob_dP[0][ke] * mobility[1] * mobility[1] + dMob_dP[1][ke] * mobility[0] * mobility[0]) / (total_mobility * total_mobility) * gravityCof[0] *
+                                   (density[0] - density[1]) +
+                                   sign[ix] * (mobility[0] * mobility[1]) / total_mobility * (dDens_dP[0][ix] - dDens_dP[1][ix]);
+
+                    real64 dG_dS =  sign[ix] * sign[ip] * (dMob_dS[0][ke] * mobility[1] * mobility[1] + dMob_dS[1][ke] * mobility[0] * mobility[0]) / (total_mobility * total_mobility) *
+                                   gravityCof[0] * (density[0] - density[1]);
+
+                    if( ix == 0 )
+                    {
+                      dG1_dS[ip][ke] = dG_dS;
+                      dhalfFlux1_dP[ip][ke] -= dG_dP;
+                      dhalfFlux1_dS[ip][ke] -= dG1_dS[ip][ke];
+                      dG1_dpc[ip][ke] = dG1_dS[ip][ke] * dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+                      // GEOS_UNUSED_VAR( dG1_dpc[ip][ke] );
+                    }
+                    else
+                    {
+                      dG2_dS[ip][ke] = dG_dS;
+                      dhalfFlux2_dP[ip][ke] -= dG_dP;
+                      dhalfFlux2_dS[ip][ke] -= dG2_dS[ip][ke];
+                      dG2_dpc[ip][ke] = dG2_dS[ip][ke] * dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+                      // GEOS_UNUSED_VAR( dG2_dpc[ip][ke] );
+                    }
+                  }
+
+                  // 3- Capillary: capillary pressure contribution
+                  capillarity[ip][ix] = -1.0 * sign[ix] * sign[ip] * mobility[0] * mobility[1] / total_mobility * (capGrad[1] -capGrad[0]);
+                  halfFluxVal[ip][ix] += capillarity[ip][ix];
+
+                  for( integer ke = 0; ke < 2; ++ke )
+                  {
+                    real64 dC_dP = sign[ix] * sign[ip] * (dMob_dP[0][ke] * mobility[1] * mobility[1] + dMob_dP[1][ke] * mobility[0] * mobility[0]) / (total_mobility * total_mobility) *
+                                   (capGrad[1] -capGrad[0]) +
+                                   sign[ix] * sign[ip] * mobility[0] * mobility[1] / total_mobility * (dCapGrad_dP[1][ke] - dCapGrad_dP[0][ke]);
+
+                    real64 dC_dS_term1 = sign[ix] * sign[ip] * (dMob_dS[0][ke] * mobility[1] * mobility[1] + dMob_dS[1][ke] * mobility[0] * mobility[0]) / (total_mobility * total_mobility) *
+                                         (capGrad[1] -capGrad[0]);
+
+                    real64 dC_dS_term2 = sign[ix] * sign[ip] * (mobility[0] * mobility[1]) / total_mobility;
+
+                    real64 dC_dS_term3 = (dCapGrad_dS[1][ke] - dCapGrad_dS[0][ke]);
+
+                    if( ix == 0 )
+                    {
+                      dC1_dS[ip][ke] = dC_dS_term1 + dC_dS_term2 * dC_dS_term3;
+                      dhalfFlux1_dP[ip][ke] -= dC_dP;
+                      dhalfFlux1_dS[ip][ke] -= dC1_dS[ip][ke];
+                      if( std::fabs( facePhaseVolFrac1[0][0] - 1.0 ) > 1e-8 )
+                      {
+                        dC1_dpc[ip][ke] =  dC1_dS[ip][ke] * dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+                      }
+                      else
+                      {
+                        dC1_dpc[ip][ke] = dC_dS_term1 * dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+                      }
+
+                      // GEOS_UNUSED_VAR( dC1_dpc[ip][ke] );
+                    }
+                    else
+                    {
+                      dC2_dS[ip][ke] = dC_dS_term1 + dC_dS_term2 * dC_dS_term3;
+                      dhalfFlux2_dP[ip][ke] -= dC_dP;
+                      dhalfFlux2_dS[ip][ke] -= dC2_dS[ip][ke];
+                      if( std::fabs( facePhaseVolFrac2[0][0] - 1.0 ) > 1e-8 )
+                      {
+                        dC2_dpc[ip][ke] =  dC2_dS[ip][ke] * dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+                      }
+                      else
+                      {
+                        dC2_dpc[ip][ke] = dC_dS_term1 * dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+                      }
+                      // GEOS_UNUSED_VAR( dC2_dpc[ip][ke] );
+                    }
+
+                  }
+
+
+                  if( halfFluxVal[ip][0] > 0.0 )
+                  {
+                    k_up_0_check[ip] = true;
+                  }
+                  if( halfFluxVal[ip][1] > 0.0 )
+                  {
+                    k_up_1_check[ip] = true;
+                  }
+
+                } // loop over phases
+
+              } // loop over half fluxes
+
+              check = true;
+
+              // Brenier and Jaffre's PPU check:
+              bool flip0[2] = {0, 0};
+              bool flip0_k_up[2] = {0, 0};
+              bool flip1[2] = {0, 0};
+              bool flip1_k_up[2] = {0, 0};
+              // loop over phases
+              for( integer ip = 0; ip < 2; ++ip )
+              {
+                bool k_up_0_b = !static_cast< bool >(k_up_0[ip]);
+                bool k_up_1_b = static_cast< bool >(k_up_1[ip]);
+                flip0_k_up[ip] =  k_up_0_b;
+                flip1_k_up[ip] =  k_up_1_b;
+
+                if( std::fabs( uT ) < 1e-20 )
+                {
+
+                  if((std::fabs( halfFluxVal[ip][0] ) < 1e-20) && (std::fabs( halfFluxVal[ip][1] ) < 1e-20))
+                  {
+                    k_up_0_check[ip] = !k_up_0_b;
+                    k_up_1_check[ip] = !k_up_1_b;
+                  }
+                  else
+                  {
+                    k_up_0_check[ip] = k_up_0_b;
+                    k_up_1_check[ip] = k_up_1_b;
+                  }
+
+                  if( k_up_0_check[ip] != k_up_0_b )
+                  {
+                    flip0[ip] = 1;
+                    check = false;
+                  }
+
+                  if( k_up_1_check[ip] != k_up_1_b )
+                  {
+                    flip1[ip] = 1;
+                    check = false;
+                  }
+
+                }
+                else
+                {
+                  if( std::fabs( halfFluxVal[ip][0] ) < 1e-20 )
+                  {
+                    k_up_0_check[ip] = k_up_0_b;
+                  }
+
+                  if( std::fabs( halfFluxVal[ip][1] ) < 1e-20 )
+                  {
+                    k_up_1_check[ip] = k_up_1_b;
+                  }
+
+                  if( k_up_0_check[ip] != k_up_0_b )
+                  {
+                    k_up_0[ip] = static_cast< localIndex >(k_up_0_b);
+                    check = false;
+                  }
+
+                  if( k_up_1_check[ip] != k_up_1_b )
+                  {
+                    k_up_1[ip] = static_cast< localIndex >(!k_up_1_b);
+                    check = false;
+                  }
+                }
+
+              }
+
+              if( flip0[0] || flip0[1] )
+              {
+                k_up_0[0] = static_cast< localIndex >(flip0_k_up[0]);
+                k_up_0[1] = static_cast< localIndex >(flip0_k_up[1]);
+              }
+
+              if( flip1[0] || flip1[1] )
+              {
+                k_up_1[0] = static_cast< localIndex >(!flip1_k_up[0]);
+                k_up_1[1] = static_cast< localIndex >(!flip1_k_up[1]);
+              }
+
+            } // while check for BJ PPU
+
+            real64 constexpr eps2 = 1.0e-18;
+            // newton update
+            dhalfFlux_dpc[0][0] = dhalfFlux1_dS[0][1]*dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+            real64 dhalfFlux_dpc00 = dV1_dpc[0][1] - dG1_dpc[0][1] - dC1_dpc[0][1];
+            dhalfFlux_dpc[0][1] = dhalfFlux2_dS[0][1]*dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+            real64 dhalfFlux_dpc01 = dV2_dpc[0][1] - dG2_dpc[0][1] - dC2_dpc[0][1];
+
+            dhalfFlux_dpc[1][0] = dhalfFlux1_dS[1][1]*dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+            real64 dhalfFlux_dpc10 = dV1_dpc[1][1] - dG1_dpc[1][1] - dC1_dpc[1][1];
+            dhalfFlux_dpc[1][1] = dhalfFlux2_dS[1][1]*dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+            real64 dhalfFlux_dpc11 = dV2_dpc[1][1] - dG2_dpc[1][1] - dC2_dpc[1][1];
+
+            dhalfFlux_dpc[0][0] = dhalfFlux_dpc00;
+            dhalfFlux_dpc[0][1] = dhalfFlux_dpc01;
+            dhalfFlux_dpc[1][0] = dhalfFlux_dpc10;
+            dhalfFlux_dpc[1][1] = dhalfFlux_dpc11;
+
+            local_jacobian = dhalfFlux_dpc[0][0] - dhalfFlux_dpc[0][1] + eps2;
+            local_residual = halfFluxVal[0][0] - halfFluxVal[0][1];
+
+            // if (iter == 1) {
+            //   grad_phi[0] = local_residual;
+            // }
+
+            // Check convergence
+            if( std::fabs( local_residual ) < tol )
+            {
+              // if( std::fabs( dhalfFlux_dpc[0][0] - dhalfFlux_dpc[0][1] ) <eps2 ) {
+              // std::cout << "**********************ZeroJacobian*******************" << std::endl;
+              // }
+              converged = 1;
+              break; // Converged
+            }
+            // converged = 0;
+            if( (!converged) && ( iter > (max_iter - 2)) )
+            {
+              if( div == 0 )
+              {
+                iter = 0;
+                div++;
+                Pc_int = Pc_min_all;
+              }
+              else if( div == 1 )
+              {
+                iter = 0;
+                div++;
+                Pc_int = Pc_max_all;
+              }
+              else if( div > 1 )
+              {
+                local_jacobian = 0.0;
+                std::cout << "**********************Diverged*******************" << std::endl;
+                iter = max_iter;
+              }
+            }
+            else
+            {
+
+              real64 deltaPc = local_residual/local_jacobian;
+
+              if( std::fabs( local_residual ) < tol )
+              {
+                // if( std::fabs( dhalfFlux_dpc[0][0] - dhalfFlux_dpc[0][1] ) < eps2 ) {
+                // std::cout << "**********************ZeroJacobian*******************" << std::endl;
+                // }
+                converged = 1;
+                break; // Converged
+              }
+
+              // Damping option:
+              if( damping )
+              {
+                real64 max_dpc = fmax( fabs( dCapPres1_dfacePhaseVolFrac[0][0][0][0] ), fabs( dCapPres2_dfacePhaseVolFrac[0][0][0][0] ));
+
+                real64 sign = std::copysign( 1.0, deltaPc );
+
+                deltaPc = fmin( fabs( deltaPc ), max_dpc * 0.2 );
+                deltaPc *= sign;
+
+              }
+
+              if( bisection && iter < 7 )
+              {
+                if( iter == 0 )
+                {
+
+                  old_Pc_int = Pc_int;
+                  Pc_int = next_Pc_int;
+                  old_residual = local_residual;
+
+                }
+                else if( old_residual * local_residual < 0.0 )
+                {
+
+                  Pc_int = (next_Pc_int + old_Pc_int) / 2.0;
+                  old_residual = local_residual;
+                  old_Pc_int = next_Pc_int;
+                  next_Pc_int = Pc_int;
+
+                }
+                else if( old_residual * local_residual > 0.0 )
+                {
+
+                  Pc_int = old_Pc_int;
+                  old_residual = local_residual;
+                  old_Pc_int = next_Pc_int;
+                  next_Pc_int = Pc_int;
+
+                }
+                else
+                {
+
+                  Pc_int = old_Pc_int;
+                  old_residual = local_residual;
+                  old_Pc_int = next_Pc_int;
+                  next_Pc_int = Pc_int;
+
+                }
+
+              }
+              else if( newton_path )
+              {
+                Pc_int -= next_Pc_int;
+
+              }
+              else
+              {
+
+                Pc_int -= deltaPc;
+
+              }
+
+
+              // truncate the updated capillary pressure (extended capillary pressure condition) for reporting/plotting:
+
+              real64 faceCapPres1_plot = fmin( Pc1_max, fmax( Pc_int, Pc1_min ));
+              real64 faceCapPres2_plot = fmin( Pc2_max, fmax( Pc_int, Pc2_min ));
+              faceCapPres1_plot = fmin( Pc2_max, fmax( faceCapPres1_plot, Pc2_min ));
+              faceCapPres2_plot = fmin( Pc1_max, fmax( faceCapPres2_plot, Pc1_min ));
+
+              // Write data to the file
+              outFile << GEOS_FMT( "{:10.10e}", local_jacobian );
+              outFile << GEOS_FMT( ",{:10.10e}", local_residual );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", Pc_int_iterate );
+              outFile << GEOS_FMT( ",{:10.10e}", faceCapPres1[0][0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", faceCapPres2[0][0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", capPres1[0][0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", capPres1[0][0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", facePhaseVolFrac1[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", facePhaseVolFrac2[0][0] );
+              outFile << std::endl;
+
+              iter++;
+
+            }
+
+
+          } // while loop
+
+          if( converged )
+          {
+
+            // Global derivatives:
+            real64 constexpr eps3 = 1.0e-18;
+
+            real64 const dPc_int_dS1 =(-1.0) * (dhalfFlux1_dS[0][0] +  dhalfFlux_duT[0][0] * duT_dS[0] - dhalfFlux_duT[0][1] * duT_dS[0]) / (dhalfFlux_dpc[0][0] - dhalfFlux_dpc[0][1] + eps3);
+            real64 const dPc_int_dS2 =(-1.0) * (dhalfFlux_duT[0][0] * duT_dS[1] - dhalfFlux2_dS[0][0] - dhalfFlux_duT[0][1] * duT_dS[1]) / (dhalfFlux_dpc[0][0] - dhalfFlux_dpc[0][1] + eps3);
+            real64 const dPc_int_du =(-1.0) * (dhalfFlux_duT[0][0]  - dhalfFlux_duT[0][1]) / (dhalfFlux_dpc[0][0] - dhalfFlux_dpc[0][1] + eps3);
+
+            dFlux_dP[0][0] =  (dhalfFlux_duT[0][0] * duT_dP[0] + dhalfFlux_dpc[0][0] * dPc_int_du * duT_dP[0]) * density2[0] + halfFluxVal[0][0] * dDens_dP2[0][0];
+            dFlux_dS[0][0] = (dhalfFlux1_dS[0][0] +  dhalfFlux_duT[0][0] * duT_dS[0] + dhalfFlux_dpc[0][0] * dPc_int_dS1) * density2[0];
+
+            dFlux_dP[0][1] = (dhalfFlux_duT[0][1] * duT_dP[1] + dhalfFlux_dpc[0][1] * dPc_int_du * duT_dP[1]) * density2[0] + halfFluxVal[0][1] * dDens_dP2[0][1];
+            dFlux_dS[0][1] = (dhalfFlux2_dS[0][0] +  dhalfFlux_duT[0][1] * duT_dS[1] + dhalfFlux_dpc[0][1] * dPc_int_dS2) * density2[0];
+
+            dFlux_dP[1][0] =  (dhalfFlux_duT[1][0] * duT_dP[0] + dhalfFlux_dpc[1][0] * dPc_int_du * duT_dP[0]) * density2[1] + halfFluxVal[1][0] * dDens_dP2[1][0];
+            dFlux_dS[1][0] = (dhalfFlux1_dS[1][0] +  dhalfFlux_duT[1][0] * duT_dS[0] + dhalfFlux_dpc[1][0] * dPc_int_dS1) * density2[1];
+
+            dFlux_dP[1][1] = (dhalfFlux_duT[1][1] * duT_dP[1] + dhalfFlux_dpc[1][1] * dPc_int_du * duT_dP[1]) * density2[1] + halfFluxVal[1][1] * dDens_dP2[1][1];
+            dFlux_dS[1][1] = (dhalfFlux2_dS[1][0] +  dhalfFlux_duT[1][1] * duT_dS[1] + dhalfFlux_dpc[1][1] * dPc_int_dS2) * density2[1];
+
+            fluxVal[0] = halfFluxVal[0][0] * density2[0];
+            fluxVal[1] = halfFluxVal[1][0] * density2[1];
+
+          }
+          else
+          {
+            std::cout << "**********************Diverged*******************" << std::endl;
+
+          }
+
+          phi[0] = fluxVal[0];
+          phi[1] = fluxVal[1];
+
+          grad_phi_P[0] = dFlux_dP[0][0];
+          grad_phi_P[1] = dFlux_dP[0][1];
+          grad_phi_P[2] = dFlux_dP[1][0];
+          grad_phi_P[3] = dFlux_dP[1][1];
+
+          grad_phi_S[0] = dFlux_dS[0][0];
+          grad_phi_S[1] = dFlux_dS[0][1];
+          grad_phi_S[2] = dFlux_dS[1][0];
+          grad_phi_S[3] = dFlux_dS[1][1];
+
+          converged = 1;
+          GEOS_UNUSED_VAR( converged );
+// Close the file after writing
+          outFile.close();
+
+        } );
+
+      } );
+
+    } );
+
+  } );
+
+
+}
 
 /******************************** FluxComputeKernelBase ********************************/
 
@@ -78,17 +1350,23 @@ class FluxComputeKernelBase
                       fields::flow::gravityCoefficient,
                       fields::immiscibleMultiphaseFlow::phaseVolumeFraction,
                       fields::immiscibleMultiphaseFlow::phaseMobility,
+                      fields::immiscibleMultiphaseFlow::phaseMass_n,
                       fields::immiscibleMultiphaseFlow::dPhaseMobility >;
 
   using MultiphaseFluidAccessors =
     StencilMaterialAccessors< constitutive::TwoPhaseImmiscibleFluid,
                               fields::twophaseimmisciblefluid::phaseDensity,
-                              fields::twophaseimmisciblefluid::dPhaseDensity >;
+                              fields::twophaseimmisciblefluid::dPhaseDensity,
+                              fields::twophaseimmisciblefluid::phaseViscosity,
+                              fields::twophaseimmisciblefluid::dPhaseViscosity >;
 
   using CapPressureAccessors =
-    StencilMaterialAccessors< CapillaryPressureBase,
+    StencilMaterialAccessors< BrooksCoreyCapillaryPressure,
                               fields::cappres::phaseCapPressure,
-                              fields::cappres::dPhaseCapPressure_dPhaseVolFraction >;
+                              fields::cappres::dPhaseCapPressure_dPhaseVolFraction
+                              >;
+  // ,fields::cappres::jFuncMultiplier >;
+
 
   using PermeabilityAccessors =
     StencilMaterialAccessors< PermeabilityBase,
@@ -135,12 +1413,16 @@ class FluxComputeKernelBase
     m_gravCoef( multiPhaseFlowAccessors.get( fields::flow::gravityCoefficient {} ) ),
     m_pres( multiPhaseFlowAccessors.get( fields::flow::pressure {} ) ),
     m_phaseVolFrac( multiPhaseFlowAccessors.get( fields::immiscibleMultiphaseFlow::phaseVolumeFraction {} ) ),
+    m_phaseMass_n( multiPhaseFlowAccessors.get( fields::immiscibleMultiphaseFlow::phaseMass_n {} ) ),
     m_mob( multiPhaseFlowAccessors.get( fields::immiscibleMultiphaseFlow::phaseMobility {} ) ),
     m_dMob( multiPhaseFlowAccessors.get( fields::immiscibleMultiphaseFlow::dPhaseMobility {} ) ),
     m_dens( fluidAccessors.get( fields::twophaseimmisciblefluid::phaseDensity {} ) ),
+    m_visc( fluidAccessors.get( fields::twophaseimmisciblefluid::phaseViscosity {} ) ),
     m_dDens_dPres( fluidAccessors.get( fields::twophaseimmisciblefluid::dPhaseDensity {} ) ),
+    m_dVisc_dPres( fluidAccessors.get( fields::twophaseimmisciblefluid::dPhaseViscosity {} ) ),
     m_phaseCapPressure( capPressureAccessors.get( fields::cappres::phaseCapPressure {} ) ),
     m_dPhaseCapPressure_dPhaseVolFrac( capPressureAccessors.get( fields::cappres::dPhaseCapPressure_dPhaseVolFraction {} ) ),
+    // m_jFuncMultiplier( capPressureAccessors.get( fields::cappres::jFuncMultiplier {} ) ),
     m_localMatrix( localMatrix ),
     m_localRhs( localRhs ),
     m_hasCapPressure ( hasCapPressure ),
@@ -174,21 +1456,26 @@ class FluxComputeKernelBase
   /// Views on pressure and phase volume fraction
   ElementViewConst< arrayView1d< real64 const > > const m_pres;
   ElementViewConst< arrayView2d< real64 const, immiscibleFlow::USD_PHASE > > const m_phaseVolFrac;
+  ElementViewConst< arrayView2d< real64 const, immiscibleFlow::USD_PHASE > > const m_phaseMass_n;
 
   /// Views on fluid mobility
   ElementViewConst< arrayView2d< real64 const, immiscibleFlow::USD_PHASE > > const m_mob;
   ElementViewConst< arrayView3d< real64 const, immiscibleFlow::USD_PHASE_DS > > const m_dMob;
 
-  /// Views on fluid density
+  /// Views on fluid density and viscosity
   ElementViewConst< arrayView3d< real64 const, constitutive::multifluid::USD_PHASE > > const m_dens;
+  ElementViewConst< arrayView3d< real64 const, constitutive::multifluid::USD_PHASE > > const m_visc;
   ElementViewConst< arrayView4d< real64 const, constitutive::multifluid::USD_PHASE_DC > > const m_dDens_dPres;
+  ElementViewConst< arrayView4d< real64 const, constitutive::multifluid::USD_PHASE_DC > > const m_dVisc_dPres;
 
   /// Views on capillary pressure
   ElementViewConst< arrayView3d< real64 const, cappres::USD_CAPPRES > > const m_phaseCapPressure;
   ElementViewConst< arrayView4d< real64 const, cappres::USD_CAPPRES_DS > > const m_dPhaseCapPressure_dPhaseVolFrac;
+  // ElementViewConst< arrayView2d< real64 const > > const m_jFuncMultiplier;
 
   // Residual and jacobian
 
+
   /// View on the local CRS matrix
   CRSMatrixView< real64, globalIndex const > const m_localMatrix;
   /// View on the local RHS
@@ -314,6 +1601,11 @@ class FluxComputeKernel : public FluxComputeKernelBase
     /// Derivatives of transmissibility with respect to pressure
     real64 dTrans_dPres[maxNumConns][2]{};
 
+    /// Transmissibility
+    real64 transmissibilityHat[maxNumConns][2]{};
+    /// Derivatives of transmissibility with respect to pressure
+    real64 dTransHat_dPres[maxNumConns][2]{};
+
     // Local degrees of freedom and local residual/jacobian
 
     /// Indices of the matrix rows/columns corresponding to the dofs in this face
@@ -372,7 +1664,7 @@ class FluxComputeKernel : public FluxComputeKernelBase
    * @param[inout] stack the stack variables
    * @param[in] NoOpFunc the function used to customize the computation of the flux
    */
-  template< typename FUNC = NoOpFunc >   // should change to multiphase
+  template< typename FUNC = NoOpFunc >    // should change to multiphase
   GEOS_HOST_DEVICE
   void computeFlux( localIndex const iconn,
                     StackVariables & stack,
@@ -437,22 +1729,22 @@ class FluxComputeKernel : public FluxComputeKernelBase
               continue;
             }
 
-            real64 const density  = m_dens[seri[ke]][sesri[ke]][sei[ke]][0][ip];                    // r = rho1 || rho2
-            real64 const dDens_dP = m_dDens_dPres[seri[ke]][sesri[ke]][sei[ke]][0][ip][Deriv::dP];  // dr/dP = dr1/dP1 || dr2/dP
+            real64 const density  = m_dens[seri[ke]][sesri[ke]][sei[ke]][0][ip];                     // r = rho1 || rho2
+            real64 const dDens_dP = m_dDens_dPres[seri[ke]][sesri[ke]][sei[ke]][0][ip][Deriv::dP];   // dr/dP = dr1/dP1 || dr2/dP
 
             // average density and derivatives
-            densMean[ip] += density;          // rho = (rho1 + rho2)
-            dDensMean_dP[ip][ke] = dDens_dP;  // drho/dP = { (dr1/dP1) , (dr2/dP2) }
+            densMean[ip] += density;           // rho = (rho1 + rho2)
+            dDensMean_dP[ip][ke] = dDens_dP;   // drho/dP = { (dr1/dP1) , (dr2/dP2) }
 
             denom++;
           }
 
           if( denom > 1 )
           {
-            densMean[ip] /= denom; // rho = (rho1 + rho2) / denom
+            densMean[ip] /= denom;  // rho = (rho1 + rho2) / denom
             for( integer ke = 0; ke < 2; ++ke )
             {
-              dDensMean_dP[ip][ke] /= denom; // drho/dP = { (dr1/dP1) / denom , (dr2/dP2) / denom }
+              dDensMean_dP[ip][ke] /= denom;  // drho/dP = { (dr1/dP1) / denom , (dr2/dP2) / denom }
             }
           }
 
@@ -471,106 +1763,114 @@ class FluxComputeKernel : public FluxComputeKernelBase
             localIndex const esr = sesri[ke];
             localIndex const ei  = sei[ke];
 
-            real64 const pressure = m_pres[er][esr][ei];      // P = P1 || P2
-            presGrad[ip] += trans[ke] * pressure;             // DPv = T (P1 - P2)
-            dPresGrad_dTrans += signPotDiff[ke] * pressure;   // dDPv/dT = (P1 - P2)
-            dPresGrad_dP[ip][ke] = trans[ke];                 // dDPv/dP = { T , -T }
+            real64 const pressure = m_pres[er][esr][ei];       // P = P1 || P2
+            presGrad[ip] += trans[ke] * pressure;              // DPv = T (P1 - P2)
+            dPresGrad_dTrans += signPotDiff[ke] * pressure;    // dDPv/dT = (P1 - P2)
+            dPresGrad_dP[ip][ke] = trans[ke];                  // dDPv/dP = { T , -T }
 
-            real64 const gravD = trans[ke] * m_gravCoef[er][esr][ei];       // D = T g z1 || -T g z2
-            real64 pot = trans[ke] * pressure - densMean[ip] * gravD; // Phi = T P1 - rho T g z1 || -T P2 + rho T g z2
+            real64 const gravD = trans[ke] * m_gravCoef[er][esr][ei];        // D = T g z1 || -T g z2
+            real64 pot = trans[ke] * pressure - densMean[ip] * gravD;  // Phi = T P1 - rho T g z1 || -T P2 + rho T g z2
 
-            gravHead[ip] += densMean[ip] * gravD;                                         // DPg = rho (T g z1 - T g z2) = T rho g (z1 - z2)
-            dGravHead_dTrans += signPotDiff[ke] * densMean[ip] * m_gravCoef[er][esr][ei]; // dDPg/dT = rho g z1 - rho g z2 = rho g (z1 - z2)
+            gravHead[ip] += densMean[ip] * gravD;                                          // DPg = rho (T g z1 - T g z2) = T rho g (z1 -
+                                                                                           // z2)
+            dGravHead_dTrans += signPotDiff[ke] * densMean[ip] * m_gravCoef[er][esr][ei];  // dDPg/dT = rho g z1 - rho g z2 = rho g (z1 -
+                                                                                           // z2)
 
             for( integer i = 0; i < 2; ++i )
             {
-              dGravHead_dP[ip][i] += dDensMean_dP[ip][i] * gravD; // dDPg/dP = {drho/dP1 * T g (z1 - z2) , drho/dP2 * T g (z1 - z2)}
+              dGravHead_dP[ip][i] += dDensMean_dP[ip][i] * gravD;  // dDPg/dP = {drho/dP1 * T g (z1 - z2) , drho/dP2 * T g (z1 - z2)}
             }
 
-            if( m_hasCapPressure )  // check sign convention
+            if( m_hasCapPressure )   // check sign convention
             {
-              real64 const capPres = m_phaseCapPressure[er][esr][ei][0][ip];  // Pc = Pc1 || Pc2
-              dCapGrad_dTrans -= signPotDiff[ke] * capPres;                   // dDPc/dT = (-Pc1 + Pc2)
-              pot -= trans[ke] * capPres;                                     // Phi = T P1 - rho T g z1 - T Pc1 || -T P2 + rho T g z2 + T
-                                                                              // Pc2
-              capGrad[ip] -= trans[ke] * capPres;                             // DPc = T (-Pc1 + Pc2)
+              real64 const capPres = m_phaseCapPressure[er][esr][ei][0][ip];   // Pc = Pc1 || Pc2
+              dCapGrad_dTrans -= signPotDiff[ke] * capPres;                    // dDPc/dT = (-Pc1 + Pc2)
+              pot -= trans[ke] * capPres;                                      // Phi = T P1 - rho T g z1 - T Pc1 || -T P2 + rho T g z2 + T
+                                                                               // Pc2
+              capGrad[ip] -= trans[ke] * capPres;                              // DPc = T (-Pc1 + Pc2)
             }
 
-            potScale = fmax( potScale, fabs( pot ) ); // maxPhi = Phi1 > Phi2 ? Phi1 : Phi2
+            potScale = fmax( potScale, fabs( pot ) );  // maxPhi = Phi1 > Phi2 ? Phi1 : Phi2
           }
 
           for( integer ke = 0; ke < 2; ++ke )
           {
-            dPresGrad_dP[ip][ke] += dTrans_dP[ke] * dPresGrad_dTrans;   // dDPv/dP = { T + dT/dP1 * (P1 - P2) , -T + dT/dP2 * (P1 - P2)}
-            dGravHead_dP[ip][ke] += dTrans_dP[ke] * dGravHead_dTrans;   // dDPg/dP = { drho/dP1 * T g (z1 - z2) + dT/dP1 * rho g (z1 - z2) ,
-                                                                        //             drho/dP2 * T g (z1 - z2) + dT/dP2 * rho g (z1 - z2) }
+            dPresGrad_dP[ip][ke] += dTrans_dP[ke] * dPresGrad_dTrans;    // dDPv/dP = { T + dT/dP1 * (P1 - P2) , -T + dT/dP2 * (P1 - P2)}
+            dGravHead_dP[ip][ke] += dTrans_dP[ke] * dGravHead_dTrans;    // dDPg/dP = { drho/dP1 * T g (z1 - z2) + dT/dP1 * rho g (z1 - z2)
+                                                                         // ,
+                                                                         //             drho/dP2 * T g (z1 - z2) + dT/dP2 * rho g (z1 - z2)
+                                                                         // }
             if( m_hasCapPressure )
             {
-              real64 const dCapPres_dS = m_dPhaseCapPressure_dPhaseVolFrac[seri[ke]][sesri[ke]][sei[ke]][0][ip][ip]; // dPc/dS = dPc1/dS1 ||
-                                                                                                                     // dPc2/dS2
-              dCapGrad_dP[ip][ke] += dTrans_dP[ke] * dCapGrad_dTrans;                                                // dDPc/dP = { dT/dP1 *
-                                                                                                                     // (-Pc1 + Pc2) ,
-                                                                                                                     //             dT/dP2 *
-                                                                                                                     // (-Pc1 + Pc2) }
-              dCapGrad_dS[ip][ke] -= trans[ke] * dCapPres_dS;                                                        // dDPc/dS = { -T *
-                                                                                                                     // dPc1/dS1 , T *
-                                                                                                                     // dPc2/dS2 }
+              real64 const dCapPres_dS = m_dPhaseCapPressure_dPhaseVolFrac[seri[ke]][sesri[ke]][sei[ke]][0][ip][ip];  // dPc/dS = dPc1/dS1
+                                                                                                                      // ||
+                                                                                                                      // dPc2/dS2
+              dCapGrad_dP[ip][ke] += dTrans_dP[ke] * dCapGrad_dTrans;                                                 // dDPc/dP = { dT/dP1
+                                                                                                                      // *
+                                                                                                                      // (-Pc1 + Pc2) ,
+                                                                                                                      //             dT/dP2
+                                                                                                                      // *
+                                                                                                                      // (-Pc1 + Pc2) }
+              dCapGrad_dS[ip][ke] -= trans[ke] * dCapPres_dS;                                                         // dDPc/dS = { -T *
+                                                                                                                      // dPc1/dS1 , T *
+                                                                                                                      // dPc2/dS2 }
             }
           }
 
           // *** upwinding ***
 
           // compute potential gradient
-          real64 potGrad = presGrad[ip] - gravHead[ip]; // DPhi = T (P1 - P2) - T rho g (z1 - z2)
+          real64 potGrad = presGrad[ip] - gravHead[ip];  // DPhi = T (P1 - P2) - T rho g (z1 - z2)
           if( m_hasCapPressure )
           {
-            potGrad += capGrad[ip]; // DPhi = T (P1 - P2) - T rho g (z1 - z2) + T (-Pc1 + Pc2)
+            potGrad += capGrad[ip];  // DPhi = T (P1 - P2) - T rho g (z1 - z2) + T (-Pc1 + Pc2)
           }
 
           // compute upwinding tolerance
           real64 constexpr upwRelTol = 1e-8;
-          real64 const upwAbsTol = fmax( potScale * upwRelTol, LvArray::NumericLimits< real64 >::epsilon ); // abstol = maxPhi * tol > eps ?
-                                                                                                            // maxPhi * tol : eps
+          real64 const upwAbsTol = fmax( potScale * upwRelTol, LvArray::NumericLimits< real64 >::epsilon );  // abstol = maxPhi * tol > eps
+                                                                                                             // ?
+                                                                                                             // maxPhi * tol : eps
 
           // decide mobility coefficients - smooth variation in [-upwAbsTol; upwAbsTol]
-          real64 const alpha = ( potGrad + upwAbsTol ) / ( 2 * upwAbsTol );   // alpha = (DPhi + abstol) / abstol / 2
+          real64 const alpha = ( potGrad + upwAbsTol ) / ( 2 * upwAbsTol );    // alpha = (DPhi + abstol) / abstol / 2
 
           // choose upstream cell
-          if( alpha <= 0.0 || alpha >= 1.0 )  // no smoothing needed
+          if( alpha <= 0.0 || alpha >= 1.0 )   // no smoothing needed
           {
-            localIndex const k_up = 1 - localIndex( fmax( fmin( alpha, 1.0 ), 0.0 ) ); // 1 upwind -> k_up = 0 || 2 upwind -> k_up = 1
+            localIndex const k_up = 1 - localIndex( fmax( fmin( alpha, 1.0 ), 0.0 ) );  // 1 upwind -> k_up = 0 || 2 upwind -> k_up = 1
 
-            mobility[ip] = m_mob[seri[k_up]][sesri[k_up]][sei[k_up]][ip];                     // M = Mupstream
-            dMob_dP[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dP];    // dM/dP = {dM/dP1 , 0} OR {0 , dM/dP2}
-            dMob_dS[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dS];    // dM/dS = {dM/dS1 , 0} OR {0 , dM/dS2}
+            mobility[ip] = m_mob[seri[k_up]][sesri[k_up]][sei[k_up]][ip];                      // M = Mupstream
+            dMob_dP[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dP];     // dM/dP = {dM/dP1 , 0} OR {0 , dM/dP2}
+            dMob_dS[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dS];     // dM/dS = {dM/dS1 , 0} OR {0 , dM/dS2}
           }
-          else  // perform smoothing
+          else   // perform smoothing
           {
             real64 const mobWeights[2] = { alpha, 1.0 - alpha };
             for( integer ke = 0; ke < 2; ++ke )
             {
-              mobility[ip] += mobWeights[ke] * m_mob[seri[ke]][sesri[ke]][sei[ke]][ip];               // M = alpha * M1 + (1 - alpha) * M2
-              dMob_dP[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dP]; // dM/dP = {alpha * dM1/dP1 , (1 -
-                                                                                                      // alpha) * dM2/dP2}
-              dMob_dS[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dS]; // dM/dP = {alpha * dM1/dS1 , (1 -
-                                                                                                      // alpha) * dM2/dS2}
+              mobility[ip] += mobWeights[ke] * m_mob[seri[ke]][sesri[ke]][sei[ke]][ip];                // M = alpha * M1 + (1 - alpha) * M2
+              dMob_dP[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dP];  // dM/dP = {alpha * dM1/dP1 , (1 -
+                                                                                                       // alpha) * dM2/dP2}
+              dMob_dS[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dS];  // dM/dP = {alpha * dM1/dS1 , (1 -
+                                                                                                       // alpha) * dM2/dS2}
             }
           }
 
           // pressure gradient depends on all points in the stencil
           for( integer ke = 0; ke < 2; ++ke )
           {
-            dFlux_dP[ip][ke] += dPresGrad_dP[ip][ke]; // dF/dP = { T + dT/dP1 * (P1 - P2) ,
-                                                      //          -T + dT/dP2 * (P1 - P2) }
+            dFlux_dP[ip][ke] += dPresGrad_dP[ip][ke];  // dF/dP = { T + dT/dP1 * (P1 - P2) ,
+                                                       //          -T + dT/dP2 * (P1 - P2) }
           }
 
           // gravitational head depends only on the two cells connected (same as mean density)
           for( integer ke = 0; ke < 2; ++ke )
           {
-            dFlux_dP[ip][ke] -= dGravHead_dP[ip][ke]; // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
-                                                      // z2) ,
-                                                      //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
-                                                      // z2) }
+            dFlux_dP[ip][ke] -= dGravHead_dP[ip][ke];  // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
+                                                       // z2) ,
+                                                       //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
+                                                       // z2) }
           }
 
           // capillary pressure contribution
@@ -578,38 +1878,38 @@ class FluxComputeKernel : public FluxComputeKernelBase
           {
             for( integer ke = 0; ke < 2; ++ke )
             {
-              dFlux_dP[ip][ke] += dCapGrad_dP[ip][ke];  // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1
-                                                        // - z2) + dT/dP1 * (-Pc1 + Pc2) ,
-                                                        //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1
-                                                        // - z2) + dT/dP2 * (-Pc1 + Pc2) }
+              dFlux_dP[ip][ke] += dCapGrad_dP[ip][ke];   // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1
+                                                         // - z2) + dT/dP1 * (-Pc1 + Pc2) ,
+                                                         //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1
+                                                         // - z2) + dT/dP2 * (-Pc1 + Pc2) }
 
-              dFlux_dS[ip][ke] += dCapGrad_dS[ip][ke];  // dF/dS = { T * -dPc/dS1 , T * dPc/dS2 }
+              dFlux_dS[ip][ke] += dCapGrad_dS[ip][ke];   // dF/dS = { T * -dPc/dS1 , T * dPc/dS2 }
             }
           }
 
           // compute the flux and derivatives using upstream cell mobility
-          fluxVal[ip] = mobility[ip] * potGrad; // F = M * DPhi
+          fluxVal[ip] = mobility[ip] * potGrad;  // F = M * DPhi
 
           for( integer ke = 0; ke < 2; ++ke )
           {
-            dFlux_dP[ip][ke] *= mobility[ip];   // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
-                                                // z2) + dT/dP1 * (-Pc1 + Pc2)] ,
-                                                //           M [-T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
-                                                // z2) + dT/dP2 * (-Pc1 + Pc2)] }
+            dFlux_dP[ip][ke] *= mobility[ip];    // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
+                                                 // z2) + dT/dP1 * (-Pc1 + Pc2)] ,
+                                                 //           M [-T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
+                                                 // z2) + dT/dP2 * (-Pc1 + Pc2)] }
 
-            dFlux_dS[ip][ke] *= mobility[ip];   // dF/dS = { M [T * -dPc/dS1] , M [T * dPc/dS2] }
+            dFlux_dS[ip][ke] *= mobility[ip];    // dF/dS = { M [T * -dPc/dS1] , M [T * dPc/dS2] }
           }
 
           // add contribution from upstream cell mobility derivatives
           for( integer ke = 0; ke < 2; ++ke )
           {
-            dFlux_dP[ip][ke] += dMob_dP[ip][ke] * potGrad;  // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho1/dP * T g (z1 - z2) - dT/dP1 *
-                                                            // rho g (z1 - z2) + dT/dP1 * (-Pc1 + Pc2)] + dM/dP1 * DPhi ,
-                                                            //           M [-T + dT/dP2 * (P1 - P2) - drho2/dP * T g (z1 - z2) - dT/dP2 *
-                                                            // rho g (z1 - z2) + dT/dP2 * (-Pc1 + Pc2)] + dM/dP2 * DPhi }
+            dFlux_dP[ip][ke] += dMob_dP[ip][ke] * potGrad;   // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho1/dP * T g (z1 - z2) - dT/dP1 *
+                                                             // rho g (z1 - z2) + dT/dP1 * (-Pc1 + Pc2)] + dM/dP1 * DPhi ,
+                                                             //           M [-T + dT/dP2 * (P1 - P2) - drho2/dP * T g (z1 - z2) - dT/dP2 *
+                                                             // rho g (z1 - z2) + dT/dP2 * (-Pc1 + Pc2)] + dM/dP2 * DPhi }
 
-            dFlux_dS[ip][ke] += dMob_dS[ip][ke] * potGrad;  // dF/dS = { M [T * -dPc/dS1] + dM/dS1 * DPhi , M [T * dPc/dS2] + dM/dS2 * DPhi
-                                                            // }
+            dFlux_dS[ip][ke] += dMob_dS[ip][ke] * potGrad;   // dF/dS = { M [T * -dPc/dS1] + dM/dS1 * DPhi , M [T * dPc/dS2] + dM/dS2 * DPhi
+                                                             // }
           }
 
           // populate local flux vector and derivatives
@@ -630,14 +1930,14 @@ class FluxComputeKernel : public FluxComputeKernelBase
           }
 
           // Customize the kernel with this lambda
-          kernelOp( k, seri, sesri, sei, connectionIndex, alpha, mobility, potGrad, fluxVal, dFlux_dP, dFlux_dS );  // Not sure what this
-                                                                                                                    // does
+          kernelOp( k, seri, sesri, sei, connectionIndex, alpha, mobility, potGrad, fluxVal, dFlux_dP, dFlux_dS );   // Not sure what this
+                                                                                                                     // does
 
-        } // loop over phases
+        }  // loop over phases
 
         connectionIndex++;
       }
-    } // loop over connection elements
+    }  // loop over connection elements
   }
 
   /**
@@ -645,7 +1945,7 @@ class FluxComputeKernel : public FluxComputeKernelBase
    * @param[in] iconn the connection index
    * @param[inout] stack the stack variables
    */
-  template< typename FUNC = NoOpFunc >                                  // should change to multiphase
+  template< typename FUNC = NoOpFunc >                                   // should change to multiphase
   GEOS_HOST_DEVICE
   void complete( localIndex const iconn,
                  StackVariables & stack,
@@ -732,6 +2032,619 @@ class FluxComputeKernel : public FluxComputeKernelBase
 };
 
 
+/**
+ * @class FaceBasedAssemblyInterfaceConditionKernel
+ * @tparam NUM_DOF number of degrees of freedom
+ * @tparam STENCILWRAPPER the type of the stencil wrapper
+ * @tparam CAPPRESWRAPPER the type of the capillary pressure wrapper
+ * @tparam RELPERMWRAPPER the type of the realtive permeability wrapper
+ * @brief Define the interface for the assembly kernel in charge of flux terms
+ */
+// template< integer NUM_EQN, integer NUM_DOF, typename STENCILWRAPPER, typename CAPPRESWRAPPER, typename RELPERMWRAPPER >
+template< integer NUM_EQN, integer NUM_DOF, typename STENCILWRAPPER >
+class FluxComputeInterfaceConditionKernel : public FluxComputeKernel< NUM_EQN, NUM_DOF, STENCILWRAPPER >
+{
+public:
+
+  using AbstractBase = FluxComputeKernelBase;
+  using DofNumberAccessor = AbstractBase::DofNumberAccessor;
+  using ImmiscibleMultiphaseFlowAccessors = AbstractBase::ImmiscibleMultiphaseFlowAccessors;
+  using MultiphaseFluidAccessors = AbstractBase::MultiphaseFluidAccessors;
+  using CapPressureAccessors = AbstractBase::CapPressureAccessors;
+  using PermeabilityAccessors = AbstractBase::PermeabilityAccessors;
+
+  using Base = FluxComputeKernel< NUM_EQN, NUM_DOF, STENCILWRAPPER >;
+  using Deriv = typename Base::Deriv;
+  using StackVariables = typename Base::StackVariables;
+  using Base::numEqn;
+  using Base::numDof;
+  using Base::m_stencilWrapper;
+  using Base::m_dofNumber;
+  using Base::m_rankOffset;
+  using Base::m_localMatrix;
+  using Base::m_localRhs;
+  using Base::m_numPhases;
+  using Base::m_permeability;
+  using Base::m_dPerm_dPres;
+  using Base::m_phaseVolFrac;
+  using Base::m_phaseMass_n;
+  using Base::m_phaseCapPressure;
+  // using Base::m_jFuncMultiplier;
+  using Base::m_dPhaseCapPressure_dPhaseVolFrac;
+  using Base::m_dens;
+  using Base::m_dDens_dPres;
+  using Base::m_visc;
+  using Base::m_dVisc_dPres;
+  using Base::m_dMob;
+  using Base::m_mob;
+  using Base::m_gravCoef;
+  using Base::m_ghostRank;
+  using Base::m_dt;
+  using Base::m_hasCapPressure;
+  using Base::m_useTotalMassEquation;
+  using Base::m_checkPhasePresenceInGravity;
+  using Base::m_seri;
+  using Base::m_sesri;
+  using Base::m_sei;
+  using Base::m_pres;
+
+  /**
+   * @brief Constructor for the kernel interface
+   * @param[in] numPhases number of fluid phases
+   * @param[in] rankOffset the offset of my MPI rank
+   * @param[in] stencilWrapper reference to the stencil wrapper
+   * @param[in] capPressureWrapper reference to the capillary pressure wrapper
+   * @param[in] dofNumberAccessor
+   * @param[in] multiPhaseFlowAccessors
+   * @param[in] fluidAccessors
+   * @param[in] capPressureAccessors
+   * @param[in] permeabilityAccessors
+   * @param[in] dt time step size
+   * @param[inout] localMatrix the local CRS matrix
+   * @param[inout] localRhs the local right-hand side vector
+   * @param[in] hasCapPressure flags for capillary pressure
+   * @param[in] useTotalMassEquation flags for using total velocity formulation
+   */
+  FluxComputeInterfaceConditionKernel( integer const numPhases,
+                                       globalIndex const rankOffset,
+                                       STENCILWRAPPER const & stencilWrapper,
+                                       //  CAPPRESWRAPPER const & capPressureWrapper,
+                                       //  RELPERMWRAPPER const & relPermWrapper,
+                                       DofNumberAccessor const & dofNumberAccessor,
+                                       ImmiscibleMultiphaseFlowAccessors const & multiPhaseFlowAccessors,
+                                       MultiphaseFluidAccessors const & fluidAccessors,
+                                       CapPressureAccessors const & capPressureAccessors,
+                                       PermeabilityAccessors const & permeabilityAccessors,
+                                       real64 const & dt,
+                                       CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                                       arrayView1d< real64 > const & localRhs,
+                                       integer const hasCapPressure,
+                                       integer const useTotalMassEquation,
+                                       integer const checkPhasePresenceInGravity,
+                                       string_array const & interfaceFaceSetNames,
+                                       stdVector< std::array< std::tuple< constitutive::RelativePermeabilityBase *,
+                                                                          constitutive::CapillaryPressureBase *,
+                                                                          constitutive::TwoPhaseImmiscibleFluid * >, 2 > > const & interfaceConstitutivePairs,
+                                       unordered_map< localIndex, localIndex > const & interfaceRegionByConnector,
+                                       //  std::tuple< constitutive::RelativePermeabilityBase *,
+                                       //              constitutive::CapillaryPressureBase *,
+                                       //              constitutive::TwoPhaseImmiscibleFluid * > const & interfaceConstitutivePairs_temp,
+                                       localIndex const GEOS_UNUSED_PARAM( domainSize ) )
+    : Base( numPhases,
+            rankOffset,
+            stencilWrapper,
+            dofNumberAccessor,
+            multiPhaseFlowAccessors,
+            fluidAccessors,
+            capPressureAccessors,
+            permeabilityAccessors,
+            dt,
+            localMatrix,
+            localRhs,
+            hasCapPressure,
+            useTotalMassEquation,
+            checkPhasePresenceInGravity ),
+    // m_capPressureWrapper( capPressureWrapper ),
+    // m_relPermWrapper( relPermWrapper ),
+    m_interfaceFaceSetNames( interfaceFaceSetNames ),
+    m_interfaceConstitutivePairs( interfaceConstitutivePairs ),
+    m_interfaceRegionByConnector( interfaceRegionByConnector )
+    // ,
+    // m_interfaceConstitutivePairs_temp( interfaceConstitutivePairs_temp )
+  {}
+
+  /**
+   * @brief Compute the local flux contributions to the residual and Jacobian
+   * @tparam FUNC the type of the function that can be used to customize the computation of the flux
+   * @param[in] iconn the connection index
+   * @param[inout] stack the stack variables
+   * @param[in] NoOpFunc the function used to customize the computation of the flux
+   */
+
+  template< typename FUNC = NoOpFunc >    // should change to multiphase
+  GEOS_HOST_DEVICE
+  void computeFlux( localIndex const iconn,
+                    StackVariables & stack,
+                    FUNC && kernelOp = NoOpFunc{} ) const
+  {
+
+    bool connectorHasInterfaceConditionQ = false;
+    bool anyInterfaceConditionsQ = not m_interfaceConstitutivePairs.empty();
+    if( anyInterfaceConditionsQ )
+    {
+      connectorHasInterfaceConditionQ =
+        m_interfaceRegionByConnector.find( iconn ) != m_interfaceRegionByConnector.end();
+    }
+
+
+
+    //  if (connectorHasInterfaceConditionQ){
+    //    // Improved transmission conditions
+    //    int ammar_code = 0;
+    //  }else{
+    //    // Regular contribution
+    //    int standard_code = 0;
+    //  }
+
+    m_stencilWrapper.computeWeights( iconn,
+                                     m_permeability,
+                                     m_dPerm_dPres,
+                                     stack.transmissibility,
+                                     stack.dTrans_dPres );
+
+    localIndex k[2];
+    localIndex connectionIndex = 0;
+
+    // one-sided transmissibility
+    m_stencilWrapper.computeHalfWeights( iconn,
+                                         m_permeability,
+                                         m_dPerm_dPres,
+                                         stack.transmissibilityHat,
+                                         stack.dTransHat_dPres );
+
+
+
+    for( k[0] = 0; k[0] < stack.numFluxElems; ++k[0] )
+    {
+      for( k[1] = k[0] + 1; k[1] < stack.numFluxElems; ++k[1] )
+      {
+        // clear working arrays
+        real64 densMean[numEqn]{};
+        real64 dDensMean_dP[numEqn][2]{};
+
+        real64 presGrad[numEqn]{};
+        real64 dPresGrad_dP[numEqn][2]{};
+
+        real64 gravHead[numEqn]{};
+        real64 dGravHead_dP[numEqn][2]{};
+
+        real64 capGrad[numEqn]{};
+        // real64 capPresIC[numEqn][2]{};
+        // real64 jFMultiplier[numEqn][2]{};
+        real64 dCapGrad_dP[numEqn][2]{};
+        real64 dCapGrad_dS[numEqn][2]{};
+
+        real64 fluxVal[numEqn]{};
+        real64 dFlux_dP[numEqn][2]{};
+        real64 dFlux_dS[numEqn][2]{};
+
+        real64 mobility[numEqn]{};
+        real64 dMob_dP[numEqn][2]{};
+        real64 dMob_dS[numEqn][2]{};
+
+        real64 density2[numEqn]{};
+        real64 dDens_dP2[numEqn][2]{};
+        real64 viscosity[numEqn]{};
+        real64 dVisc_dP[numEqn][2]{};
+        real64 gravCoef2[numEqn]{};
+        real64 gravCoefHat[numEqn]{};
+
+        real64 uT = 0;
+        // real64 total_mobility = 0;
+        real64 duT_dP[numEqn]{};
+        real64 duT_dS[numEqn]{};
+
+        real64 potGrad_ip[numEqn]{};
+        real64 alpha_ip[numEqn]{};
+
+        real64 const trans[2] = { stack.transmissibility[connectionIndex][0], stack.transmissibility[connectionIndex][1] };
+        real64 const dTrans_dP[2] = { stack.dTrans_dPres[connectionIndex][0], stack.dTrans_dPres[connectionIndex][1] };
+
+        real64 const transHat[2] = { stack.transmissibilityHat[connectionIndex][0], stack.transmissibilityHat[connectionIndex][1] * -1.0};
+        real64 const dTransHat_dP[2] = { stack.dTransHat_dPres[connectionIndex][0], stack.dTransHat_dPres[connectionIndex][1] * -1.0};
+
+        // cell indices
+        localIndex const seri[2]  = {m_seri( iconn, k[0] ), m_seri( iconn, k[1] )};
+        localIndex const sesri[2] = {m_sesri( iconn, k[0] ), m_sesri( iconn, k[1] )};
+        localIndex const sei[2]   = {m_sei( iconn, k[0] ), m_sei( iconn, k[1] )};
+
+        stdVector< real64 > saturations = {m_phaseVolFrac[seri[0]][sesri[0]][sei[0]][0], m_phaseVolFrac[seri[1]][sesri[1]][sei[1]][0] };
+        stdVector< real64 > pressures = {m_pres[seri[0]][sesri[0]][sei[0]], m_pres[seri[1]][sesri[1]][sei[1]] };
+        // bool isJfunction = 0;
+
+        // loop over phases
+        for( integer ip = 0; ip < m_numPhases; ++ip )
+        {
+          // calculate quantities on primary connected cells
+          integer denom = 0;
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            // density
+            bool const phaseExists = (m_phaseVolFrac[seri[ke]][sesri[ke]][sei[ke]][ip] > 0);
+            if( m_checkPhasePresenceInGravity && !phaseExists )
+            {
+              continue;
+            }
+
+            real64 const density  = m_dens[seri[ke]][sesri[ke]][sei[ke]][0][ip];         // r = rho1 || rho2
+            real64 const dDens_dP = m_dDens_dPres[seri[ke]][sesri[ke]][sei[ke]][0][ip][Deriv::dP]; // dr/dP = dr1/dP1 || dr2/dP
+            // average density and derivatives
+            densMean[ip] += density; // rho = (rho1 + rho2)
+            dDensMean_dP[ip][ke] = dDens_dP; // drho/dP = { (dr1/dP1) , (dr2/dP2) }
+            denom++;
+          }
+
+          if( denom > 1 )
+          {
+            densMean[ip] /= denom; // rho = (rho1 + rho2) / denom
+            for( integer ke = 0; ke < 2; ++ke )
+            {
+              dDensMean_dP[ip][ke] /= denom; // drho/dP = { (dr1/dP1) / denom , (dr2/dP2) / denom }
+            }
+          }
+
+          //***** calculation of flux *****
+
+          // compute potential difference
+          real64 potScale = 0.0;
+          real64 dPresGrad_dTrans = 0.0;
+          real64 dGravHead_dTrans = 0.0;
+          real64 dCapGrad_dTrans = 0.0;
+          gravCoefHat[0] = 0;
+          gravCoefHat[1] = 0;
+          constexpr int signPotDiff[2] = {1, -1};
+
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            localIndex const er  = seri[ke];
+            localIndex const esr = sesri[ke];
+            localIndex const ei  = sei[ke];
+
+            real64 const pressure = m_pres[er][esr][ei]; // P = P1 || P2
+            presGrad[ip] += trans[ke] * pressure;  // DPv = T (P1 - P2)
+            dPresGrad_dTrans += signPotDiff[ke] * pressure; // dDPv/dT = (P1 - P2)
+            dPresGrad_dP[ip][ke] = trans[ke];      // dDPv/dP = { T , -T }
+
+            real64 const gravD = trans[ke] * m_gravCoef[er][esr][ei]; // D = T g z1 || -T g z2
+            real64 pot = trans[ke] * pressure - densMean[ip] * gravD; // Phi = T P1 - rho T g z1 || -T P2 + rho T g z2
+            gravCoefHat[0] += m_gravCoef[er][esr][ei] * 0.5;
+            gravCoefHat[1] += m_gravCoef[er][esr][ei] * 0.5;
+
+            gravCoef2[ke] = m_gravCoef[er][esr][ei];
+
+            gravHead[ip] += densMean[ip] * gravD;                              // DPg = rho (T g z1 - T g z2) = T rho g (z1 - z2)
+            dGravHead_dTrans += signPotDiff[ke] * densMean[ip] * m_gravCoef[er][esr][ei]; // dDPg/dT = rho g z1 - rho g z2 = rho g (z1 - z2)
+
+            for( integer i = 0; i < 2; ++i )
+            {
+              dGravHead_dP[ip][i] += dDensMean_dP[ip][i] * gravD; // dDPg/dP = {drho/dP1 * T g (z1 - z2) , drho/dP2 * T g (z1 - z2)}
+            }
+
+            if( m_hasCapPressure ) // check sign convention
+            {
+              real64 const capPres = m_phaseCapPressure[er][esr][ei][0][ip]; // Pc = Pc1 || Pc2
+              // jFMultiplier[ip][ke] = m_jFuncMultiplier[er][esr][ei][0];
+
+              // capPresIC[ip][ke] = capPres;
+              dCapGrad_dTrans -= signPotDiff[ke] * capPres;      // dDPc/dT = (-Pc1 + Pc2)
+              pot -= trans[ke] * capPres;                        // Phi = T P1 - rho T g z1 - T Pc1 || -T P2 + rho T g z2 + T
+              // Pc2
+              capGrad[ip] -= trans[ke] * capPres;                // DPc = T (-Pc1 + Pc2)
+            }
+
+            potScale = fmax( potScale, fabs( pot ) ); // maxPhi = Phi1 > Phi2 ? Phi1 : Phi2
+          }
+
+
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            dPresGrad_dP[ip][ke] += dTrans_dP[ke] * dPresGrad_dTrans; // dDPv/dP = { T + dT/dP1 * (P1 - P2) , -T + dT/dP2 * (P1 - P2)}
+            dGravHead_dP[ip][ke] += dTrans_dP[ke] * dGravHead_dTrans; // dDPg/dP = { drho/dP1 * T g (z1 - z2) + dT/dP1 * rho g (z1 - z2) ,
+            //             drho/dP2 * T g (z1 - z2) + dT/dP2 * rho g (z1 - z2) }
+            if( m_hasCapPressure )
+            {
+              real64 const dCapPres_dS = m_dPhaseCapPressure_dPhaseVolFrac[seri[ke]][sesri[ke]][sei[ke]][0][ip][ip]; // dPc/dS = dPc1/dS1 ||
+              // dPc2/dS2
+              dCapGrad_dP[ip][ke] += dTrans_dP[ke] * dCapGrad_dTrans;                                   // dDPc/dP = { dT/dP1 *
+              // (-Pc1 + Pc2) ,
+              //             dT/dP2 *
+              // (-Pc1 + Pc2) }
+              dCapGrad_dS[ip][ke] -= trans[ke] * dCapPres_dS;                                           // dDPc/dS = { -T *
+              // dPc1/dS1 , T *
+              // dPc2/dS2 }
+            }
+          }
+
+          // *** upwinding ***
+          // compute potential gradient
+          real64 potGrad = presGrad[ip] - gravHead[ip]; // DPhi = T (P1 - P2) - T rho g (z1 - z2)
+          if( m_hasCapPressure )
+          {
+            potGrad += capGrad[ip]; // DPhi = T (P1 - P2) - T rho g (z1 - z2) + T (-Pc1 + Pc2)
+          }
+
+          // compute upwinding tolerance
+          real64 constexpr upwRelTol = 1e-8;
+          real64 const upwAbsTol = fmax( potScale * upwRelTol, LvArray::NumericLimits< real64 >::epsilon ); // abstol = maxPhi * tol > eps ?
+          // maxPhi * tol : eps
+
+          // decide mobility coefficients - smooth variation in [-upwAbsTol; upwAbsTol]
+          real64 alpha = ( potGrad + upwAbsTol ) / ( 2 * upwAbsTol ); // alpha = (DPhi + abstol) / abstol / 2
+
+          // choose upstream cell
+          if( alpha <= 0.0 || alpha >= 1.0 ) // no smoothing needed
+          {
+            localIndex const k_up = 1 - localIndex( fmax( fmin( alpha, 1.0 ), 0.0 ) ); // 1 upwind -> k_up = 0 || 2 upwind -> k_up = 1
+
+            mobility[ip] = m_mob[seri[k_up]][sesri[k_up]][sei[k_up]][ip];          // M = Mupstream
+            density2[ip] = m_dens[seri[k_up]][sesri[k_up]][sei[k_up]][0][ip];         // r = rho1 || rho2
+            dDens_dP2[ip][k_up] = m_dDens_dPres[seri[k_up]][sesri[k_up]][sei[k_up]][0][ip][Deriv::dP]; // dr/dP = dr1/dP1 || dr2/dP
+            viscosity[ip]  = m_visc[seri[k_up]][sesri[k_up]][sei[k_up]][0][ip];
+            dVisc_dP[ip][k_up] = m_dVisc_dPres[seri[k_up]][sesri[k_up]][sei[k_up]][0][ip][Deriv::dP];
+            dMob_dP[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dP]; // dM/dP = {dM/dP1 , 0} OR {0 , dM/dP2}
+            dMob_dS[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dS]; // dM/dS = {dM/dS1 , 0} OR {0 , dM/dS2}
+          }
+          else // perform smoothing
+          {
+            real64 const mobWeights[2] = { alpha, 1.0 - alpha };
+            for( integer ke = 0; ke < 2; ++ke )
+            {
+              mobility[ip] += mobWeights[ke] * m_mob[seri[ke]][sesri[ke]][sei[ke]][ip];  // M = alpha * M1 + (1 - alpha) * M2
+              density2[ip] += mobWeights[ke] * m_dens[seri[ke]][sesri[ke]][sei[ke]][0][ip];       // r = rho1 || rho2
+              dDens_dP2[ip][ke] = mobWeights[ke] * m_dDens_dPres[seri[ke]][sesri[ke]][sei[ke]][0][ip][Deriv::dP]; // dr/dP = dr1/dP1 ||
+              // dr2/dP
+              viscosity[ip]  = m_visc[seri[ke]][sesri[ke]][sei[ke]][0][ip];
+              dVisc_dP[ip][ke] = m_dVisc_dPres[seri[ke]][sesri[ke]][sei[ke]][0][ip][Deriv::dP];
+              dMob_dP[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dP]; // dM/dP = {alpha * dM1/dP1 , (1 -
+              // alpha) * dM2/dP2}
+              dMob_dS[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dS]; // dM/dP = {alpha * dM1/dS1 , (1 -
+              // alpha) * dM2/dS2}
+            }
+          }
+
+          // pressure gradient depends on all points in the stencil
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            dFlux_dP[ip][ke] += dPresGrad_dP[ip][ke]; // dF/dP = { T + dT/dP1 * (P1 - P2) ,
+            //          -T + dT/dP2 * (P1 - P2) }
+          }
+
+          // gravitational head depends only on the two cells connected (same as mean density)
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            dFlux_dP[ip][ke] -= dGravHead_dP[ip][ke]; // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
+            // z2) ,
+            //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
+            // z2) }
+          }
+
+          // capillary pressure contribution
+          if( m_hasCapPressure )
+          {
+            for( integer ke = 0; ke < 2; ++ke )
+            {
+              dFlux_dP[ip][ke] += dCapGrad_dP[ip][ke]; // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1
+              // - z2) + dT/dP1 * (-Pc1 + Pc2) ,
+              //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1
+              // - z2) + dT/dP2 * (-Pc1 + Pc2) }
+
+              dFlux_dS[ip][ke] += dCapGrad_dS[ip][ke]; // dF/dS = { T * -dPc/dS1 , T * dPc/dS2 }
+            }
+          }
+
+          // compute the flux and derivatives using upstream cell mobility
+          fluxVal[ip] = mobility[ip] * potGrad; // F = M * DPhi
+
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            dFlux_dP[ip][ke] *= mobility[ip]; // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
+            // z2) + dT/dP1 * (-Pc1 + Pc2)] ,
+            //           M [-T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
+            // z2) + dT/dP2 * (-Pc1 + Pc2)] }
+
+            dFlux_dS[ip][ke] *= mobility[ip]; // dF/dS = { M [T * -dPc/dS1] , M [T * dPc/dS2] }
+          }
+
+          // add contribution from upstream cell mobility derivatives
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+
+            real64 dMob_dP2 = mobility[ip] / density2[ip] * (-dVisc_dP[ip][ke] / viscosity[ip]);
+
+            duT_dP[ke] += dFlux_dP[ip][ke] / density2[ip] + dMob_dP2 * potGrad;
+
+            dFlux_dP[ip][ke] += dMob_dP[ip][ke] * potGrad; // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho1/dP * T g (z1 - z2) - dT/dP1 *
+            // rho g (z1 - z2) + dT/dP1 * (-Pc1 + Pc2)] + dM/dP1 * DPhi ,
+            //           M [-T + dT/dP2 * (P1 - P2) - drho2/dP * T g (z1 - z2) - dT/dP2 *
+            // rho g (z1 - z2) + dT/dP2 * (-Pc1 + Pc2)] + dM/dP2 * DPhi }
+            dFlux_dS[ip][ke] += dMob_dS[ip][ke] * potGrad; // dF/dS = { M [T * -dPc/dS1] + dM/dS1 * DPhi , M [T * dPc/dS2] + dM/dS2 * DPhi
+            // }
+          }
+
+
+          uT += fluxVal[ip] / density2[ip];
+
+          // add contribution from upstream cell mobility derivatives
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+//  duT_dP[ke] += dFlux_dP[ip][ke] - fluxVal[ip] * dDens_dP2[ip][ke] / density2[ip];
+//  // duT_dP[ke] += dFlux_dP[ip][ke];
+
+//  duT_dP[ke]  /= density2[ip];
+
+            duT_dS[ke] += dFlux_dS[ip][ke] / density2[ip];
+            // duT_dS[ke] += dFlux_dS[ip][ke];
+
+          }
+
+          potGrad_ip[ip] = potGrad;
+          alpha_ip[ip] = alpha;
+
+        } // loop over phases
+
+
+        // this determines whether the local solver is needed becuase of heterogeneous capillary pressure regions
+        // bool notOnInterface = std::fabs( jFMultiplier[0][0] - jFMultiplier[0][1] ) < 1  && std::fabs( jFMultiplier[1][0] -
+        // jFMultiplier[1][1] ) < 1;
+        bool notOnInterface = !connectorHasInterfaceConditionQ;
+        if( notOnInterface )
+        {
+          for( integer ip = 0; ip < 2; ++ip )
+          {
+            // populate local flux vector and derivatives
+            stack.localFlux[k[0]*numEqn + ip] += m_dt * fluxVal[ip];
+            stack.localFlux[k[1]*numEqn + ip] -= m_dt * fluxVal[ip];
+
+            for( integer ke = 0; ke < 2; ++ke )
+            {
+              // pressure
+              localIndex const localDofIndexPres = k[ke] * numDof;
+              stack.localFluxJacobian[k[0]*numEqn + ip][localDofIndexPres] += m_dt * dFlux_dP[ip][ke];
+              stack.localFluxJacobian[k[1]*numEqn + ip][localDofIndexPres] -= m_dt * dFlux_dP[ip][ke];
+
+              // saturation
+              localIndex const localDofIndexSat = k[ke] * numDof + 1;
+              stack.localFluxJacobian[k[0]*numEqn + ip][localDofIndexSat] += m_dt * dFlux_dS[ip][ke];
+              stack.localFluxJacobian[k[1]*numEqn + ip][localDofIndexSat] -= m_dt * dFlux_dS[ip][ke];
+            }
+
+            // Customize the kernel with this lambda
+            kernelOp( k, seri, sesri, sei, connectionIndex, alpha_ip[ip], mobility, potGrad_ip[ip], fluxVal, dFlux_dP, dFlux_dS );
+
+          }
+        }
+        else
+        {
+
+
+          bool converged = 0;
+
+
+          // clear working arrays
+          real64 halfFluxVal[numEqn][2]{};
+          // real64 dhalfFlux1_dP[numEqn][2]{};
+          // real64 dhalfFlux1_dS[numEqn][2]{};
+          // real64 dhalfFlux2_dP[numEqn][2]{};
+          // real64 dhalfFlux2_dS[numEqn][2]{};
+          // real64 dhalfFlux_duT[numEqn][2]{};
+          // real64 dhalfFlux_dpc[numEqn][2]{};
+
+
+          // stdVector< real64 > JFMultipliers = {jFMultiplier[0][0], jFMultiplier[0][1]};
+          stdVector< real64 > JFMultipliers = {0.0, 0.0};
+          stdVector< real64 > trappedSats1 = {0.0, 0.0};
+          stdVector< real64 > trappedSats2 = {0.0, 0.0};
+          stdVector< real64 > transHats = {transHat[0], transHat[1]};
+          stdVector< real64 > dTransHats_dP = {dTransHat_dP[0], dTransHat_dP[1]};
+          stdVector< real64 > gravCoefHats = {gravCoefHat[0], gravCoefHat[1]};
+          stdVector< real64 > gravCoefs = {gravCoef2[0], gravCoef2[1]};
+          stdVector< real64 > cellCenterDuTdS = {duT_dP[0], duT_dP[1], duT_dS[0], duT_dS[1]};
+          stdVector< real64 > cellCenterDens = {density2[0], density2[1]};
+          stdVector< real64 > cellCenterDens_dP = {dDens_dP2[0][0], dDens_dP2[0][1], dDens_dP2[1][0], dDens_dP2[1][1]};
+          // std::vector< RelativePermeabilityBase * > relPerms = {std::get< 0 >( m_interfaceConstitutivePairs_temp ), std::get< 0 >(
+          // m_interfaceConstitutivePairs_temp )};
+          // std::vector< CapillaryPressureBase * > capPressures = {std::get< 1 >( m_interfaceConstitutivePairs_temp ), std::get< 1 >(
+          // m_interfaceConstitutivePairs_temp )};
+          // std::vector< TwoPhaseImmiscibleFluid * > fluids = {std::get< 2 >( m_interfaceConstitutivePairs_temp ), std::get< 2 >(
+          // m_interfaceConstitutivePairs_temp )};
+
+          // auto const & pairArray = m_interfaceConstitutivePairs[0];
+          localIndex const surfaceRegionIndex = m_interfaceRegionByConnector.at( iconn );
+          auto const & pairArray = m_interfaceConstitutivePairs[surfaceRegionIndex];
+
+          std::vector< constitutive::RelativePermeabilityBase * > relPerms = {
+            std::get< 0 >( pairArray[0] ),
+            std::get< 0 >( pairArray[1] )
+          };
+
+          std::vector< constitutive::CapillaryPressureBase * > capPressures = {
+            std::get< 1 >( pairArray[0] ),
+            std::get< 1 >( pairArray[1] )
+          };
+
+          std::vector< constitutive::TwoPhaseImmiscibleFluid * > fluids = {
+            std::get< 2 >( pairArray[0] ),
+            std::get< 2 >( pairArray[1] )
+          };
+
+          stdVector< real64 > phi = {halfFluxVal[0][0], halfFluxVal[0][1]};
+          stdVector< real64 > grad_phi_P = {0.0, 0.0, 0.0, 0.0};
+          stdVector< real64 > grad_phi_S = {0.0, 0.0, 0.0, 0.0};
+
+          local_solver( uT, saturations, pressures, JFMultipliers, trappedSats1, trappedSats2, transHats, dTransHats_dP, gravCoefHats, gravCoefs,
+                        cellCenterDuTdS, cellCenterDens, cellCenterDens_dP, relPerms, capPressures, fluids, phi, grad_phi_P, grad_phi_S, converged );
+
+
+          fluxVal[0] = phi[0];
+          fluxVal[1] = phi[1];
+          dFlux_dP[0][0] = grad_phi_P[0];
+          dFlux_dP[0][1] = grad_phi_P[1];
+          dFlux_dP[1][0] = grad_phi_P[2];
+          dFlux_dP[1][1] = grad_phi_P[3];
+          dFlux_dS[0][0] = grad_phi_S[0];
+          dFlux_dS[0][1] = grad_phi_S[1];
+          dFlux_dS[1][0] = grad_phi_S[2];
+          dFlux_dS[1][1] = grad_phi_S[3];
+
+          // Global residual and jacobian update:
+          for( integer ip = 0; ip < m_numPhases; ++ip )
+          {
+            // populate local flux vector and derivatives
+            stack.localFlux[k[0]*numEqn + ip] += m_dt * fluxVal[ip];
+            stack.localFlux[k[1]*numEqn + ip] -= m_dt * fluxVal[ip];
+
+            for( integer ke = 0; ke < 2; ++ke )
+            {
+              // pressure
+              localIndex const localDofIndexPres = k[ke] * numDof;
+              stack.localFluxJacobian[k[0]*numEqn + ip][localDofIndexPres] += m_dt * dFlux_dP[ip][ke];
+              stack.localFluxJacobian[k[1]*numEqn + ip][localDofIndexPres] -= m_dt * dFlux_dP[ip][ke];
+
+              // saturation
+              localIndex const localDofIndexSat = k[ke] * numDof + 1;
+              stack.localFluxJacobian[k[0]*numEqn + ip][localDofIndexSat] += m_dt * dFlux_dS[ip][ke];
+              stack.localFluxJacobian[k[1]*numEqn + ip][localDofIndexSat] -= m_dt * dFlux_dS[ip][ke];
+            }
+
+            // Customize the kernel with this lambda
+            kernelOp( k, seri, sesri, sei, connectionIndex, alpha_ip[ip], mobility, potGrad_ip[ip], fluxVal, dFlux_dP, dFlux_dS );
+
+          } // loop over phases
+        } // end of else for interface conditions
+
+        connectionIndex++;
+      }
+    } // loop over connection elements
+  }
+
+protected:
+
+  /// Reference to the capillary pressure wrapper
+  // CAPPRESWRAPPER const m_capPressureWrapper;
+  // RELPERMWRAPPER const m_relPermWrapper;
+  string_array const m_interfaceFaceSetNames;
+  stdVector< std::array< std::tuple< constitutive::RelativePermeabilityBase *,
+                                     constitutive::CapillaryPressureBase *,
+                                     constitutive::TwoPhaseImmiscibleFluid * >, 2 > >  const m_interfaceConstitutivePairs;
+  unordered_map< localIndex, localIndex > const m_interfaceRegionByConnector;
+  // std::tuple< constitutive::RelativePermeabilityBase *,
+  //             constitutive::CapillaryPressureBase *,
+  //             constitutive::TwoPhaseImmiscibleFluid * > const m_interfaceConstitutivePairs_temp;
+
+};
+
+
+
 /****************************************** */
 
 /**
@@ -788,6 +2701,74 @@ class FluxComputeKernelFactory
                        checkPhasePresenceInGravity );
     kernelType::template launch< POLICY >( stencilWrapper.size(), kernel );
   }
+
+  /**
+   * @brief Create a new kernel and launch
+   * @tparam POLICY the policy used in the RAJA kernel
+   * @tparam STENCILWRAPPER the type of the stencil wrapper
+   * @tparam CAPPRESWRAPPER the type of the capillary pressure wrapper
+   * @param[in] rankOffset the offset of my MPI rank
+   * @param[in] dofKey string to get the element degrees of freedom numbers
+   * @param[in] solverName name of the solver (to name accessors)
+   * @param[in] elemManager reference to the element region manager
+   * @param[in] stencilWrapper reference to the stencil wrapper
+   * @param[in] capPresWrapper reference to the capillary pressure wrapper
+   * @param[in] dt time step size
+   * @param[inout] localMatrix the local CRS matrix
+   * @param[inout] localRhs the local right-hand side vector
+   */
+  // template< typename POLICY, typename STENCILWRAPPER, typename CAPPRESWRAPPER, typename RELPERMWRAPPER >
+  template< typename POLICY, typename STENCILWRAPPER >
+  static void
+  createAndLaunch( integer const numPhases,
+                   globalIndex const rankOffset,
+                   string const & dofKey,
+                   integer const hasCapPressure,
+                   integer const useTotalMassEquation,
+                   integer const checkPhasePresenceInGravity,
+                   string const & solverName,
+                   ElementRegionManager const & elemManager,
+                   STENCILWRAPPER const & stencilWrapper,
+                   //  CAPPRESWRAPPER const & capPresWrapper,
+                   //  RELPERMWRAPPER const & relPermWrapper,
+                   string_array const & interfaceFaceSetNames,
+                   stdVector< std::array< std::tuple< constitutive::RelativePermeabilityBase *,
+                                                      constitutive::CapillaryPressureBase *,
+                                                      constitutive::TwoPhaseImmiscibleFluid * >, 2 > > const & interfaceConstitutivePairs,
+                   unordered_map< localIndex, localIndex > const & interfaceRegionByConnector,
+                   //  std::tuple< constitutive::RelativePermeabilityBase *,
+                   //              constitutive::CapillaryPressureBase *,
+                   //              constitutive::TwoPhaseImmiscibleFluid * > const & interfaceConstitutivePairs_temp,
+                   ElementSubRegionBase const & subRegion,
+                   real64 const & dt,
+                   CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                   arrayView1d< real64 > const & localRhs )
+  {
+    integer constexpr NUM_EQN = 2;
+    integer constexpr NUM_DOF = 2;
+    localIndex const domainSize = subRegion.size();
+    ElementRegionManager::ElementViewAccessor< arrayView1d< globalIndex const > > dofNumberAccessor =
+      elemManager.constructArrayViewAccessor< globalIndex, 1 >( dofKey );
+    dofNumberAccessor.setName( solverName + "/accessors/" + dofKey );
+
+    // using kernelType = FluxComputeInterfaceConditionKernel< NUM_EQN, NUM_DOF, STENCILWRAPPER, CAPPRESWRAPPER, RELPERMWRAPPER >;
+    using kernelType = FluxComputeInterfaceConditionKernel< NUM_EQN, NUM_DOF, STENCILWRAPPER >;
+    typename kernelType::ImmiscibleMultiphaseFlowAccessors flowAccessors( elemManager, solverName );
+    typename kernelType::MultiphaseFluidAccessors fluidAccessors( elemManager, solverName );
+    typename kernelType::CapPressureAccessors capPressureAccessors( elemManager, solverName );
+    typename kernelType::PermeabilityAccessors permAccessors( elemManager, solverName );
+
+    // kernelType kernel( numPhases, rankOffset, stencilWrapper, capPresWrapper, relPermWrapper, dofNumberAccessor,
+    //                    flowAccessors, fluidAccessors, capPressureAccessors, permAccessors,
+    //                    dt, localMatrix, localRhs, hasCapPressure, useTotalMassEquation,
+    //                    checkPhasePresenceInGravity, interfaceFaceSetNames, interfaceConstitutivePairs, interfaceRegionByConnector,
+    // interfaceConstitutivePairs_temp, domainSize );
+    kernelType kernel( numPhases, rankOffset, stencilWrapper, dofNumberAccessor,
+                       flowAccessors, fluidAccessors, capPressureAccessors, permAccessors,
+                       dt, localMatrix, localRhs, hasCapPressure, useTotalMassEquation,
+                       checkPhasePresenceInGravity, interfaceFaceSetNames, interfaceConstitutivePairs, interfaceRegionByConnector, domainSize );
+    kernelType::template launch< POLICY >( stencilWrapper.size(), kernel );
+  }
 };
 
 
@@ -795,7 +2776,7 @@ class FluxComputeKernelFactory
 
 enum class KernelFlags
 {
-  TotalMassEquation = 1 << 0, // 1
+  TotalMassEquation = 1 << 0,  // 1
 
   /// Add more flags like that if needed:
   // Flag2 = 1 << 1, // 2
@@ -1421,7 +3402,7 @@ class ResidualNormKernelFactory
     {
       ResidualNormKernel::launchLinf< POLICY >( subRegion.size(), kernel, residualNorm );
     }
-    else // L2 norm
+    else  // L2 norm
     {
       ResidualNormKernel::launchL2< POLICY >( subRegion.size(), kernel, residualNorm, residualNormalizer );
     }
@@ -1431,9 +3412,9 @@ class ResidualNormKernelFactory
 
 
 
-} // namespace immiscible multiphasekernels
+}  // namespace immiscible multiphasekernels
 
 
-} // namespace geos
+}  // namespace geos
 
-#endif //GEOS_PHYSICSSOLVERS_FLUIDFLOW_MULTIPHASEKERNELS_HPP
+ #endif //GEOS_PHYSICSSOLVERS_FLUIDFLOW_MULTIPHASEKERNELS_HPP