Thomas saigre patch 1

examples/modules/fsi/pages/lid-driven-cavity/README.adoc

@@ -9,12 +9,12 @@ Computer codes, used for the acquisition of results, are from Vincent <<Chabanne
 
 This benchmark has aso been realized by <<Gerbeau>>, <<Vàzquez>>, <<Kuttler>> and <<Kassiotis>>.
 
-== Problem Description 
+== Problem Description
 
 We study here an incompressible fluid flowing into a cavity, where its walls are elastic. We use the following geometry to represent it.
 
 [[img-geometry1]]
-image::lid-driven-cavity/LidDriven.png[caption="Figure 1 : ", title="Geometry of lid-driven cavity flow.", alt="LidDriven Geometry", width="600", align="center"]  
+image::lid-driven-cavity/LidDriven.png[caption="Figure 1 : ", title="Geometry of lid-driven cavity flow.", alt="LidDriven Geometry", width="600", align="center"]
 
 The domain stem:[\Omega_f^*] is define by a square stem:[ [0,1\]^2 ], stem:[\Gamma^{i,*}_f] and stem:[\Gamma^{o,*}_f] are respectively the flow entrance and the flow outlet.
 A constant flow velocity, following the stem:[x] axis, will be imposed on stem:[\Gamma_f^{h,*}] border, while a null flow velocity will be imposed on stem:[\Gamma_f^{f,*}]. This last point represent also a non-slip condition for the fluid.
@@ -23,7 +23,7 @@ Furthermore, we add a structure domain, at the bottom of the fluid one, named st
 
 During this test, we will observe the displacement of a point stem:[A], positioned at stem:[(0;0.5)], into the stem:[y] direction, and compare our results to ones found in other references.
 
-=== Boundary conditions 
+=== Boundary conditions
 
 Before enunciate the boundary conditions, we need to describe a oscillatory velocity, following the $$x$$ axis and dependent of time.
 
@@ -32,7 +32,7 @@ Before enunciate the boundary conditions, we need to describe a oscillatory velo
   v_{in} = 1-cos\left( \frac{2\pi t}{5} \right)
 ++++
 
-Then we can set 
+Then we can set
 
 * on stem:[\Gamma^{h,*}_f], an inflow Dirichlet condition : stem:[\boldsymbol{u}_{f} = ( v_{in}, 0 )]
 
@@ -46,30 +46,30 @@ Then we can set
 
 * on stem:[\Gamma^{e,*}_s], a condition that lets these boundaries be free from constraints : stem:[\boldsymbol{F}_{s} \boldsymbol{\Sigma}_s \boldsymbol{n}_s = \boldsymbol{0}]
 
-To them we also add the fluid-structure coupling conditions on stem:[\Gamma_{fsi}^*] : 
+To them we also add the fluid-structure coupling conditions on stem:[\Gamma_{fsi}^*] :
 
 [stem]
 ++++
 \frac{\partial \boldsymbol{\eta_{s}} }{\partial t} - \boldsymbol{u}_f \circ \mathcal{A}^t_f
-  = \boldsymbol{0} \quad \left( \text{Velocities continuity}\right) 
+  = \boldsymbol{0} \quad \left( \text{Velocities continuity}\right)
 ++++
 
 [stem]
 ++++
   \boldsymbol{F}_{s} \boldsymbol{\Sigma}_{s} \boldsymbol{n}^*_s + J_{\mathcal{A}^t_f} \boldsymbol{F}_{\mathcal{A}^t_f}^{-T} \hat{\boldsymbol{\sigma}}_f \boldsymbol{n}^*_f
-  = \boldsymbol{0} \quad \left( \text{ Constraint continuity}\right) 
+  = \boldsymbol{0} \quad \left( \text{ Constraint continuity}\right)
 ++++
 
 [stem]
 ++++
   \boldsymbol{\varphi}_s^t  - \mathcal{A}^t_f
-  = \boldsymbol{0} \quad \left( \text{Geometric continuity}\right) 
+  = \boldsymbol{0} \quad \left( \text{Geometric continuity}\right)
 ++++
 
 === Initial conditions
 
 To realize the simulations, we used a time step stem:[\Delta t] equals to stem:[0.01] s.
-    
+
 == Inputs
 
 The following table displays the various fixed and variables
@@ -82,7 +82,7 @@ parameters of this test-case.
 |stem:[E_s] | Young's modulus | stem:[250]  | stem:[N.m^{-2}]
 |stem:[\nu_s] | Poisson's ratio | stem:[0]  | dimensionless
 |stem:[\rho_s] | structure density | stem:[500]  |stem:[kg.m^{-3}]
-|stem:[\mu_f] |viscosity | stem:[1\times 10^{-3}]  |stem:[m^2.s^{-1}] 
+|stem:[\mu_f] |viscosity | stem:[1\times 10^{-3}]  |stem:[m^2.s^{-1}]
 |stem:[\rho_f] | density | stem:[1] | stem:[kg.m^{-3}]
 |===
 
@@ -95,7 +95,7 @@ To discretize space, we used stem:[P_N~-~P_{N-1}] Taylor-Hood finite elements.
 
 For the structure time discretization,  Newmark-beta method is the one we used. And for the fluid time discretization, we used BDF, at order stem:[q].
 
-== Implementation 
+== Implementation
 
 All the codes files are into https://github.com/feelpp/feelpp/tree/develop/toolboxes/feel/feelmodels/fsi[FSI]
 
@@ -113,13 +113,13 @@ Then we retry with a stem:[P_3~-~P_2] approximation for the fluid with a geometr
 |
 |===
 
-Finally we launch it with the same conditions as before, but with a deformed interface. 
+Finally we launch it with the same conditions as before, but with a deformed interface.
 
 |===
 |
 |===
 
-=== Conclusion 
+=== Conclusion
 
 First at all, we can see that the first two tests offer us similar results, despite different orders uses. At contrary, the third result set are better than the others.
 
@@ -136,7 +136,7 @@ The elastic wall thinness, in the stable case, should give an important refineme
 
 - [[[Gerbeau]]] J.F. Gerbeau, M. Vidrascu, et al, _A quasi-newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows_, 2003.
 
-- [[[Vazquez]]] J.G. Valdés Vazquèz et al, _Nonlinear analysis of orthotropic membrane and shell structures including fluid-structure interaction_, 2007.
+- [[[Vàzquez]]] J.G. Valdés Vazquèz et al, _Nonlinear analysis of orthotropic membrane and shell structures including fluid-structure interaction_, 2007.
 
 - [[[KuttlerWall]]] U. Kuttler and W.A. Wall, _Fixed-point fluid–structure interaction solvers with dynamic relaxation_, Computational Mechanics, 2008.
 

toolboxes/modules/ROOT/pages/modeling-analysis-using-json-files.adoc

@@ -1,7 +1,4 @@
-= 2. Modeling and Analysis using the JSON files
-:page-tags: manual
-:page-illustration: pass:[toolboxes::manual.svg]
-:description: We present the JSON files used to configure the physical models and the analysis.
+= Modeling and Analysis using the JSON files
 
 The Model JSON (`.json`) files allow to configure a set of partial differential equations, more precisely they define:
 
@@ -362,7 +359,7 @@ We denote by stem:[f] the distance function computed and stem:[g] a normalizatio
 
 [stem]
 ++++
-g(f)=a+\frac{\left(f-min(f)\right)\left(b-a\right)}{max(f)-min(f)}
+g(f)=a+\frac{\left(f-\min(f)\right)\left(b-a\right)}{\max(f)-\min(f)}
 ++++
 
 with reals stem:[a] and stem:[b] (should verify stem:[a<b]) specifying the range of values (default stem:[[0,1]]).
@@ -371,7 +368,7 @@ with reals stem:[a] and stem:[b] (should verify stem:[a<b]) specifying the range
 
 [stem]
 ++++
-g(f)=\frac{f-average(f)}{max(f)-min(f)}
+g(f)=\frac{f-\mathrm{average}(f)}{\max(f)-\min(f)}
 ++++
 
 .Example 1 of DistanceToRange normalisation setup
@@ -393,8 +390,9 @@ g(f)=\frac{f-average(f)}{max(f)-min(f)}
 }
 ----
 The previous snippet JSON will generate two normalizations of the distance function by using :
-* min_max method with default range stem:[\left[0,1\right]] : generated symbol is `meshes_<mesh_id>_distanceToRange_walls_normalized_min_max`.
-* mean method : generated symbol is `meshes_<mesh_id>_distanceToRange_walls_normalized_mean`.
+
+* `min_max` method with default range stem:[[0, 1\]] : generated symbol is `meshes_<mesh_id>_distanceToRange_walls_normalized_min_max`.
+* `mean` method : generated symbol is `meshes_<mesh_id>_distanceToRange_walls_normalized_mean`.
 
 .Example 2 of DistanceToRange normalisation setup
 [source,json]
@@ -406,7 +404,7 @@ The previous snippet JSON will generate two normalizations of the distance funct
   }
 }
 ----
-The previous snippet JSON will generated one normalization Min-Max of the distance function on interval stem:[\left[1,2\rifht]].
+The previous snippet JSON will generated one normalization Min-Max of the distance function on interval stem:[[1,2\]].
 
 
 .Example 3 of DistanceToRange normalisation setup
@@ -1210,7 +1208,7 @@ The quadrature order used in the norm computed can be also given if an analytica
 <11> coordinates of the point
 <12> fields to be computed at the point coordinate
 
-Here is a   xref:toolboxes:csm:rotating-winch/index.adoc[biele example] from the Toolbox examples.
+Here is a xref:cases:csm:rotating-winch/index.adoc[biele example] from the Toolbox examples.
 
 
 == The generator of cases by using the index definitions