From ff8c8211f0272c26b785aff9b448e5de5cb48412 Mon Sep 17 00:00:00 2001 From: Michael Duncan Walker Date: Mon, 16 Jun 2025 09:21:28 -0700 Subject: [PATCH 1/3] implement analytical IC to hydrostatic equilibrium --- examples/RT3D.py | 89 +++++++++++++++++++++++++------------ examples/RTI_dPdZ_init.pdf | Bin 0 -> 258195 bytes 2 files changed, 61 insertions(+), 28 deletions(-) create mode 100644 examples/RTI_dPdZ_init.pdf diff --git a/examples/RT3D.py b/examples/RT3D.py index 0132a62..2231134 100644 --- a/examples/RT3D.py +++ b/examples/RT3D.py @@ -25,7 +25,6 @@ test = False - ## Define a mesh if is2D: problem = 'RT_2D' @@ -62,7 +61,7 @@ 'mwH':mwH,'mwL':mwL, 'Runiv':Runiv,'waveLength':waveLength, 'rho_l':rho_l,'rho_h':rho_h, - 'delta':2.0* numpy.pi / Npts * 4 } + 'delta':2.0* numpy.pi / Npts * 4.0 } # Initialize a simulation object on a mesh ss = pyrandaSim(problem,imesh) @@ -82,7 +81,6 @@ def meanXto3d(pysim,data): ss.addUserDefinedFunction("xbar",meanXto3d) - # Define the equations of motion eom =""" # Primary Equations of motion here @@ -161,15 +159,15 @@ def meanXto3d(pysim,data): bc.const(['Yh'],['x1'],0.0) bc.const(['Yl'],['x1'],1.0) bc.const(['Yl'],['xn'],0.0) -bc.extrap(['rho','Et'],['x1','xn']) +# bc.extrap(['rho','Et'],['x1','xn']) bc.const(['u','v','w'],['x1','xn'],0.0) # Sponge BCs -:leftBC: = 1.0 - 0.5 * (1.0 + tanh( (meshx-1.0) / .1 ) ) -:rightBC: = 0.5 * (1.0 + tanh( (meshx-8.0) / .1 ) ) -:BC: = numpy.maximum(:leftBC:,:rightBC:) -:u: = gbar(:u:)*:BC: + :u:*(1.0 - :BC:) -:rho: = gbar(:rho:)*:BC: + :rho:*(1.0 - :BC:) -:Et: = gbar(:Et:)*:BC: + :Et:*(1.0 - :BC:) +#:leftBC: = 1.0 - 0.5 * (1.0 + tanh( (meshx-1.0) / .1 ) ) +#:rightBC: = 0.5 * (1.0 + tanh( (meshx-8.0) / .1 ) ) +#:BC: = numpy.maximum(:leftBC:,:rightBC:) +#:u: = gbar(:u:)*:BC: + :u:*(1.0 - :BC:) +#:rho: = gbar(:rho:)*:BC: + :rho:*(1.0 - :BC:) +#:Et: = gbar(:Et:)*:BC: + :Et:*(1.0 - :BC:) :rhoYh: = :rho:*:Yh: :rhoYl: = :rho:*:Yl: :rhou: = :rho:*:u: @@ -186,27 +184,55 @@ def meanXto3d(pysim,data): ic = """ :gamma:= 5./3. p0 = 1.0 -At = ( (rho_h - rho_l)/(rho_h + rho_l) ) -u0 = sqrt( abs(gx*At/waveLength) ) * .1 +# At = ( (rho_h - rho_l)/(rho_h + rho_l) ) +u0 = 0.0 # sqrt( abs(gx*At/waveLength) ) * 0.1 # velocity oscillations deprecated MDW in favor of perturbed surface +T0 = 1.0 +offset = 1.4*pi + 0.5 * sin(2 * meshy) # surface perturbed with sine wave MDW -# Add interface -:Yl: = .5 * (1.0-tanh( sqrt(pi)*( meshx - 1.4*pi ) / delta )) -:Yh: = 1.0 - :Yl: -:p: += p0 +# Add smooth/diffuse interface +:Yh: = 0.5 * (1.0 + tanh( (meshx-offset) / delta )) +:Yl: = 1.0 - :Yh: + +# Define R mixture +:mw: = 1.0 / ( :Yh: / mwH + :Yl: / mwL ) +:R: = Runiv / :mw: +R_l = Runiv / mwL +R_h = Runiv / mwH + +# Define analytical solution for pressure for hydrostatic equilibrium (see RTI_dPdZ_init file for derivation) +A = gx * (R_h + R_l) / (2.0 * Runiv * T0 * R_l * R_h) +B = gx * delta * (R_l - R_h) / (2.0 * Runiv * T0 * R_l * R_h) +:p: = p0 * exp(A * (meshx-offset)) * (numpy.cosh( (meshx-offset) / delta ))**(B) + +# If no diffuse interface, Yl,Yh are just constants +# :p: = p0 * exp(( gx * (R_h * :Yl: + R_l * :Yh:) / (2.0 * Runiv * T0 * R_l * R_h)) * (meshx-offset)) + +# # Pressure initial pressure distribution +# def P_init(meshx,gx,rho_h,rho_l,offset,p0): +# if ( meshx <= offset): +# P = p0 + rho_l * gx * (meshx-offset) +# if ( meshx > offset): +# P = p0 - rho_h * gx * (meshx-offset) +# return P +# Define ideal profile +# :p: = P_init(meshx,gx,rho_h,rho_l,offset,p0) # Add oscillations near interface wgt = 4*:Yh:*:Yl: -:v: *= 0.0 -:w: *= 0.0 -:u: = wgt * gbar( (random3D()-0.5)*u0 ) - -:rho: = rho_h * :Yh: + rho_l * :Yl: +:v: = 3d(0.0) +:w: = 3d(0.0) +:u: = 3d(0.0) # wgt * gbar( (random3D()-0.5)*u0 ) # velocity oscillations deprecated MDW in favor of perturbed surface + +# Primitive variables +:T: = 3d(T0) +# :T: = :p: / (:rho: * :R: ) +:rho: = :p: / ( :R: * :T: ) # rho_h * :Yh: + rho_l * :Yl: # deprecated MDW +:error: = ddx(:p:) - :rho:*gx :cv: = :Yh:*CVh + :Yl:*CVl :cp: = :Yh:*CPh + :Yl:*CPl :gamma: = :cp:/:cv: -:mw: = 1.0 / ( :Yh: / mwH + :Yl: / mwL ) -:R: = Runiv / :mw: -:T: = :p: / (:rho: * :R: ) +:cs: = sqrt( :p: / :rho: * :gamma: ) +:dt: = dt.courant(:u:,:v:,:w:,:cs:) # Form conserved quatities :rhoYh: = :rho:*:Yh: @@ -215,8 +241,6 @@ def meanXto3d(pysim,data): :rhov: = :rho:*:v: :rhow: = :rho:*:w: :Et: = :p: / (:gamma:-1.0) + 0.5*:rho:*(:u:*:u: + :v:*:v: + :w:*:w:) -:cs: = sqrt( :p: / :rho: * :gamma: ) -:dt: = dt.courant(:u:,:v:,:w:,:cs:) """ # Set the initial conditions @@ -261,7 +285,7 @@ def meanXto3d(pysim,data): timeW.append( time ) if not test: - if ( ss.cycle%viz_freq == 0 ) : + if (ss.cycle%viz_freq == 0 ) : #True) : # replace with True to plot each timestep # 2D contour plots ss.plot.figure(1) @@ -269,8 +293,17 @@ def meanXto3d(pysim,data): ss.plot.contourf( 'rho', 32, cmap='jet') ss.plot.figure(2) + ss.plot.clf() # comment these lines to have each timestep plot overlayed + ss.plot.plot('error') + + ss.plot.figure(3) + ss.plot.clf() + 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zNbk5YuNh;NcE%s2180MNGKS#x;bih&s-e)btj$Wr`JSGUUx7#z7kWfp#s^}ec z+yY;*@Ai>l){}I5I_Frv{)2{z|4qYGoP4}>VP2|mHxIZw%-x6MJco!X+!gL+;9+eG z+NcJ*>0}Gj@Ur&*C!M$qb8>L>;gFOT=MXXQwej)y0H3$g3-IW#>{oQp5QPIEa`+Tj~-aUKv)IB4;a-e}f18@KH^XCy5lX=0}3jGIT zVM$S8acK?<%3V0LoNmH6KuaVo_&8iVtbH84Vb&Zse|}V2SW;LNG(^`6Zs%)DxykOA z|N0K_Uxr@R9v(0|V2IYP-Y|;c{F-W#f7A7!MyC(6|7~W{QvbwwcW0umwU?VW2W6T9 z%lCD2_vQfC>w3ZLoNOs0Bqk1S1+16DoI{L50{pcEmhKb);}8RvT~XsOSFn?o5tp#F zhlxqr*xO3lNu8IKk&v*lk(7|KmKC+OmQYd Date: Wed, 18 Jun 2025 14:41:20 -0700 Subject: [PATCH 2/3] fix error with universal gas constant --- examples/RT3D.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/examples/RT3D.py b/examples/RT3D.py index 2231134..0378cfe 100644 --- a/examples/RT3D.py +++ b/examples/RT3D.py @@ -200,12 +200,12 @@ def meanXto3d(pysim,data): R_h = Runiv / mwH # Define analytical solution for pressure for hydrostatic equilibrium (see RTI_dPdZ_init file for derivation) -A = gx * (R_h + R_l) / (2.0 * Runiv * T0 * R_l * R_h) -B = gx * delta * (R_l - R_h) / (2.0 * Runiv * T0 * R_l * R_h) +A = gx * (R_h + R_l) / (2.0 * T0 * R_l * R_h) +B = gx * delta * (R_l - R_h) / (2.0 * T0 * R_l * R_h) :p: = p0 * exp(A * (meshx-offset)) * (numpy.cosh( (meshx-offset) / delta ))**(B) # If no diffuse interface, Yl,Yh are just constants -# :p: = p0 * exp(( gx * (R_h * :Yl: + R_l * :Yh:) / (2.0 * Runiv * T0 * R_l * R_h)) * (meshx-offset)) +# :p: = p0 * exp(( gx * (R_h * :Yl: + R_l * :Yh:) / (2.0 * T0 * R_l * R_h)) * (meshx-offset)) # # Pressure initial pressure distribution # def P_init(meshx,gx,rho_h,rho_l,offset,p0): From 09551a3f3b8007e31ea08b95cd9a1131bbb0554a Mon Sep 17 00:00:00 2001 From: Michael Duncan Walker Date: Thu, 19 Jun 2025 13:45:55 -0700 Subject: [PATCH 3/3] fix gas constant error in derivation --- examples/RTI_dPdZ_init.pdf | Bin 258195 -> 273859 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/examples/RTI_dPdZ_init.pdf b/examples/RTI_dPdZ_init.pdf index 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