twoPhaseEulerFoam: transform to solve for p_rgh

to avoid excessive pressure/buoyancy balance errors on non-orthogonal meshes
Resolves bug-report http://openfoam.org/mantisbt/view.php?id=1379

applications/solvers/multiphase/twoPhaseEulerFoam/createFields.H

+    #include "readGravitationalAcceleration.H"
+    #include "readhRef.H"
+
     Info<< "Creating twoPhaseSystem\n" << endl;
 
     twoPhaseSystem fluid(mesh, g);
@@ -27,6 +30,13 @@
         fluid.lookup("pMin")
     );
 
+
+    Info<< "Calculating field g.h\n" << endl;
+    dimensionedScalar ghRef(g & (cmptMag(g.value())/mag(g.value()))*hRef);
+    volScalarField gh("gh", (g & mesh.C()) - ghRef);
+    surfaceScalarField ghf("ghf", (g & mesh.Cf()) - ghRef);
+
+
     rhoThermo& thermo1 = phase1.thermo();
     rhoThermo& thermo2 = phase2.thermo();
 
@@ -38,6 +48,20 @@
     volScalarField& rho2 = thermo2.rho();
     const volScalarField& psi2 = thermo2.psi();
 
+    Info<< "Reading field p_rgh\n" << endl;
+    volScalarField p_rgh
+    (
+        IOobject
+        (
+            "p_rgh",
+            runTime.timeName(),
+            mesh,
+            IOobject::MUST_READ,
+            IOobject::AUTO_WRITE
+        ),
+        mesh
+    );
+
     volVectorField U
     (
         IOobject
@@ -99,7 +123,14 @@
 
     label pRefCell = 0;
     scalar pRefValue = 0.0;
-    setRefCell(p, pimple.dict(), pRefCell, pRefValue);
+    setRefCell
+    (
+        p,
+        p_rgh,
+        pimple.dict(),
+        pRefCell,
+        pRefValue
+    );
 
     Info<< "Creating field dpdt\n" << endl;
     volScalarField dpdt

applications/solvers/multiphase/twoPhaseEulerFoam/pEqn.H

@@ -28,49 +28,60 @@
     mrfZones.makeAbsolute(phi2);
 
     // Phase-1 pressure flux (e.g. due to particle-particle pressure)
-    surfaceScalarField phiP1
+    surfaceScalarField phiF1
     (
-        "phiP1",
+        "phiF1",
         fvc::interpolate(rAU1*phase1.turbulence().pPrime())
        *fvc::snGrad(alpha1)*mesh.magSf()
     );
-    phiP1.boundaryField() == 0;
+    phiF1.boundaryField() == 0;
 
     // Phase-2 pressure flux (e.g. due to particle-particle pressure)
-    surfaceScalarField phiP2
+    surfaceScalarField phiF2
     (
-        "phiP2",
+        "phiF2",
         fvc::interpolate(rAU2*phase2.turbulence().pPrime())
        *fvc::snGrad(alpha2)*mesh.magSf()
     );
-    phiP2.boundaryField() == 0;
-
+    phiF2.boundaryField() == 0;
+
+    volScalarField rho("rho", fluid.rho());
+    surfaceScalarField ghSnGradRho(ghf*fvc::snGrad(rho)*mesh.magSf());
+
+    // Add the phase-1 buoyancy force
+    phiF1 +=
+        rAlphaAU1f
+       *(
+            ghSnGradRho
+          - alpha2f*fvc::interpolate(rho1 - rho2)*(g & mesh.Sf())
+        )/fvc::interpolate(rho1);
+
+    // Add the phase-2 buoyancy force
+    phiF2 +=
+        rAlphaAU2f
+       *(
+            ghSnGradRho
+          - alpha1f*fvc::interpolate(rho2 - rho1)*(g & mesh.Sf())
+        )/fvc::interpolate(rho2);
+
+    // Phase-1 predicted flux
     surfaceScalarField phiHbyA1
     (
         IOobject::groupName("phiHbyA", phase1.name()),
         (fvc::interpolate(HbyA1) & mesh.Sf())
       + rAlphaAU1f*fvc::ddtCorr(U1, phi1)
+      + fvc::interpolate(rAU1*dragCoeff)*phi2
+      - phiF1
     );
 
+    // Phase-2 predicted flux
     surfaceScalarField phiHbyA2
     (
         IOobject::groupName("phiHbyA", phase2.name()),
         (fvc::interpolate(HbyA2) & mesh.Sf())
       + rAlphaAU2f*fvc::ddtCorr(U2, phi2)
-    );
-
-    phiHbyA1 +=
-    (
-        fvc::interpolate(rAU1*dragCoeff)*phi2
-      - phiP1
-      + rAlphaAU1f*(g & mesh.Sf())
-    );
-
-    phiHbyA2 +=
-    (
-        fvc::interpolate(rAU2*dragCoeff)*phi1
-      - phiP2
-      + rAlphaAU2f*(g & mesh.Sf())
+      + fvc::interpolate(rAU2*dragCoeff)*phi1
+      - phiF2
     );
 
     mrfZones.makeRelative(phiHbyA1);
@@ -98,7 +109,7 @@
     // Update the fixedFluxPressure BCs to ensure flux consistency
     setSnGrad<fixedFluxPressureFvPatchScalarField>
     (
-        p.boundaryField(),
+        p_rgh.boundaryField(),
         (
             phiHbyA.boundaryField()
           - mrfZones.relative
@@ -134,8 +145,8 @@
             )/rho1
           + (alpha1/rho1)*correction
             (
-                psi1*fvm::ddt(p)
-              + fvm::div(phid1, p) - fvm::Sp(fvc::div(phid1), p)
+                psi1*fvm::ddt(p_rgh)
+              + fvm::div(phid1, p_rgh) - fvm::Sp(fvc::div(phid1), p_rgh)
             );
         deleteDemandDrivenData(pEqnComp1().faceFluxCorrectionPtr());
         pEqnComp1().relax();
@@ -147,8 +158,8 @@
             )/rho2
           + (alpha2/rho2)*correction
             (
-                psi2*fvm::ddt(p)
-              + fvm::div(phid2, p) - fvm::Sp(fvc::div(phid2), p)
+                psi2*fvm::ddt(p_rgh)
+              + fvm::div(phid2, p_rgh) - fvm::Sp(fvc::div(phid2), p_rgh)
             );
         deleteDemandDrivenData(pEqnComp2().faceFluxCorrectionPtr());
         pEqnComp2().relax();
@@ -160,31 +171,31 @@
                 contErr1
               - fvc::Sp(fvc::ddt(alpha1) + fvc::div(alphaPhi1), rho1)
             )/rho1
-          + (alpha1*psi1/rho1)*correction(fvm::ddt(p));
+          + (alpha1*psi1/rho1)*correction(fvm::ddt(p_rgh));
 
         pEqnComp2 =
             (
                 contErr2
               - fvc::Sp(fvc::ddt(alpha2) + fvc::div(alphaPhi2), rho2)
             )/rho2
-          + (alpha2*psi2/rho2)*correction(fvm::ddt(p));
+          + (alpha2*psi2/rho2)*correction(fvm::ddt(p_rgh));
     }
 
     // Cache p prior to solve for density update
-    volScalarField p_0(p);
+    volScalarField p_rgh_0(p_rgh);
 
     while (pimple.correctNonOrthogonal())
     {
         fvScalarMatrix pEqnIncomp
         (
             fvc::div(phiHbyA)
-          - fvm::laplacian(rAUf, p)
+          - fvm::laplacian(rAUf, p_rgh)
         );
 
         solve
         (
             pEqnComp1() + pEqnComp2() + pEqnIncomp,
-            mesh.solver(p.select(pimple.finalInnerIter()))
+            mesh.solver(p_rgh.select(pimple.finalInnerIter()))
         );
 
         if (pimple.finalNonOrthogonalIter())
@@ -209,22 +220,22 @@
 
             fluid.dgdt() =
             (
-                alpha1*(pEqnComp2 & p)
-              - alpha2*(pEqnComp1 & p)
+                alpha1*(pEqnComp2 & p_rgh)
+              - alpha2*(pEqnComp1 & p_rgh)
             );
 
-            p.relax();
+            p_rgh.relax();
+
+            p = max(p_rgh + rho*gh, pMin);
+            p_rgh = p - rho*gh;
+
             mSfGradp = pEqnIncomp.flux()/rAUf;
 
             U1 = HbyA1
               + fvc::reconstruct
                 (
-                    rAlphaAU1f
-                   *(
-                        (g & mesh.Sf())
-                      + mSfGradp/fvc::interpolate(rho1)
-                    )
-                  - phiP1
+                    rAlphaAU1f*mSfGradp/fvc::interpolate(rho1)
+                  - phiF1
                 );
             U1.correctBoundaryConditions();
             fvOptions.correct(U1);
@@ -232,12 +243,8 @@
             U2 = HbyA2
               + fvc::reconstruct
                 (
-                    rAlphaAU2f
-                   *(
-                        (g & mesh.Sf())
-                      + mSfGradp/fvc::interpolate(rho2)
-                    )
-                  - phiP2
+                    rAlphaAU2f*mSfGradp/fvc::interpolate(rho2)
+                  - phiF2
                 );
             U2.correctBoundaryConditions();
             fvOptions.correct(U2);
@@ -246,11 +253,9 @@
         }
     }
 
-    p = max(p, pMin);
-
     // Update densities from change in p
-    rho1 += psi1*(p - p_0);
-    rho2 += psi2*(p - p_0);
+    rho1 += psi1*(p_rgh - p_rgh_0);
+    rho2 += psi2*(p_rgh - p_rgh_0);
 
     K1 = 0.5*magSqr(U1);
     K2 = 0.5*magSqr(U2);

applications/solvers/multiphase/twoPhaseEulerFoam/twoPhaseEulerFoam.C

@@ -49,7 +49,6 @@ int main(int argc, char *argv[])
 
     pimpleControl pimple(mesh);
 
-    #include "readGravitationalAcceleration.H"
     #include "createFields.H"
     #include "createMRFZones.H"
     #include "createFvOptions.H"

tutorials/multiphase/twoPhaseEulerFoam/LES/bubbleColumn/0/p

@@ -22,17 +22,17 @@ boundaryField
 {
     inlet
     {
-        type               fixedFluxPressure;
+        type               calculated;
         value              $internalField;
     }
     outlet
     {
-        type               fixedValue;
+        type               calculated;
         value              $internalField;
     }
     walls
     {
-        type               fixedFluxPressure;
+        type               calculated;
         value              $internalField;
     }
 }

tutorials/multiphase/twoPhaseEulerFoam/LES/bubbleColumn/0/p_rgh

+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  dev                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volScalarField;
+    object      p_rgh;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions          [ 1 -1 -2 0 0 0 0 ];
+
+internalField       uniform 1e5;
+
+boundaryField
+{
+    inlet
+    {
+        type               fixedFluxPressure;
+        value              $internalField;
+    }
+    outlet
+    {
+        type               fixedValue;
+        value              $internalField;
+    }
+    walls
+    {
+        type               fixedFluxPressure;
+        value              $internalField;
+    }
+}
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

tutorials/multiphase/twoPhaseEulerFoam/LES/bubbleColumn/system/fvSchemes

@@ -61,7 +61,7 @@ snGradSchemes
 fluxRequired
 {
     default         no;
-    p               ;
+    p_rgh;
 }
 
 

tutorials/multiphase/twoPhaseEulerFoam/LES/bubbleColumn/system/fvSolution

@@ -23,7 +23,7 @@ solvers
         nAlphaSubCycles 2;
     }
 
-    p
+    p_rgh
     {
         solver          GAMG;
         smoother        DIC;
@@ -38,9 +38,9 @@ solvers
         relTol          0.01;
     }
 
-    pFinal
+    p_rghFinal
     {
-        $p;
+        $p_rgh;
         relTol          0;
     }
 

tutorials/multiphase/twoPhaseEulerFoam/RAS/bubbleColumn/0/p

@@ -22,17 +22,17 @@ boundaryField
 {
     inlet
     {
-        type               fixedFluxPressure;
+        type               calculated;
         value              $internalField;
     }
     outlet
     {
-        type               fixedValue;
+        type               calculated;
         value              $internalField;
     }
     walls
     {
-        type               fixedFluxPressure;
+        type               calculated;
         value              $internalField;
     }
 }

tutorials/multiphase/twoPhaseEulerFoam/RAS/bubbleColumn/0/p_rgh

+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  dev                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volScalarField;
+    object      p_rgh;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions          [ 1 -1 -2 0 0 0 0 ];
+
+internalField       uniform 1e5;
+
+boundaryField
+{
+    inlet
+    {
+        type               fixedFluxPressure;
+        value              $internalField;
+    }
+    outlet
+    {
+        type               fixedValue;
+        value              $internalField;
+    }
+    walls
+    {
+        type               fixedFluxPressure;
+        value              $internalField;
+    }
+}
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

tutorials/multiphase/twoPhaseEulerFoam/RAS/bubbleColumn/system/fvSchemes

@@ -63,7 +63,7 @@ snGradSchemes
 fluxRequired
 {
     default         no;
-    p               ;
+    p_rgh;
 }
 
 

tutorials/multiphase/twoPhaseEulerFoam/RAS/bubbleColumn/system/fvSolution

@@ -23,7 +23,7 @@ solvers
         nAlphaSubCycles 2;
     }
 
-    p
+    p_rgh
     {
         solver          GAMG;
         smoother        DIC;
@@ -38,9 +38,9 @@ solvers
         relTol          0.01;
     }
 
-    pFinal
+    p_rghFinal
     {
-        $p;
+        $p_rgh;
         relTol          0;
     }
 

tutorials/multiphase/twoPhaseEulerFoam/RAS/fluidisedBed/0/p

@@ -14,7 +14,7 @@ FoamFile
 }
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
-dimensions          [ 1 -1 -2 0 0 0 0 ];
+dimensions          [1 -1 -2 0 0 0 0];
 
 internalField       uniform 1e5;
 
@@ -22,19 +22,19 @@ boundaryField
 {
     inlet
     {
-        type               fixedFluxPressure;
+        type               calculated;
         value              $internalField;
     }
 
     outlet
     {
-        type               fixedValue;
+        type               calculated;
         value              $internalField;
     }
 
     walls
     {
-        type               fixedFluxPressure;
+        type               calculated;
         value              $internalField;
     }
 

tutorials/multiphase/twoPhaseEulerFoam/RAS/fluidisedBed/0/p_rgh

+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  dev                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volScalarField;
+    object      p_rgh;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions          [1 -1 -2 0 0 0 0];
+
+internalField       uniform 1e5;
+
+boundaryField
+{
+    inlet
+    {
+        type               fixedFluxPressure;
+        value              $internalField;
+    }
+
+    outlet
+    {
+        type               fixedValue;
+        value              $internalField;
+    }
+
+    walls
+    {
+        type               fixedFluxPressure;
+        value              $internalField;
+    }
+
+    frontAndBackPlanes
+    {
+        type               empty;
+    }
+}
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

tutorials/multiphase/twoPhaseEulerFoam/RAS/fluidisedBed/system/fvSchemes

@@ -68,7 +68,7 @@ snGradSchemes
 fluxRequired
 {
     default     no;
-    p           ;
+    p_rgh;
     alpha.particles;
 }
 

tutorials/multiphase/twoPhaseEulerFoam/RAS/fluidisedBed/system/fvSolution

@@ -30,7 +30,7 @@ solvers
         minIter         1;
     }
 
-    p
+    p_rgh
     {
         solver          GAMG;
         smoother        DIC;
@@ -45,9 +45,9 @@ solvers
         relTol          0.01;
     }
 
-    pFinal
+    p_rghFinal
     {
-        $p;
+        $p_rgh;
         relTol          0;
     }
 

tutorials/multiphase/twoPhaseEulerFoam/laminar/bubbleColumn/0/p

@@ -22,17 +22,17 @@ boundaryField
 {
     inlet
     {
-        type               fixedFluxPressure;
+        type               calculated;
         value              $internalField;
     }
     outlet
     {
-        type               fixedValue;
+        type               calculated;
         value              $internalField;
     }
     walls
     {
-        type               fixedFluxPressure;
+        type               calculated;
         value              $internalField;
     }
 }

tutorials/multiphase/twoPhaseEulerFoam/laminar/bubbleColumn/0/p_rgh

+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  dev                                   |
+|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    version     2.0;
+    format      ascii;
+    class       volScalarField;
+    object      p_rgh;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+dimensions          [ 1 -1 -2 0 0 0 0 ];
+
+internalField       uniform 1e5;
+
+boundaryField
+{
+    inlet
+    {
+        type               fixedFluxPressure;
+        value              $internalField;
+    }
+    outlet
+    {
+        type               fixedValue;
+        value              $internalField;
+    }
+    walls
+    {
+        type               fixedFluxPressure;
+        value              $internalField;
+    }
+}
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

tutorials/multiphase/twoPhaseEulerFoam/laminar/bubbleColumn/system/fvSchemes

@@ -60,7 +60,7 @@ snGradSchemes
 fluxRequired
 {
     default         no;
-    p               ;
+    p_rgh;
 }
 
 

tutorials/multiphase/twoPhaseEulerFoam/laminar/bubbleColumn/system/fvSolution

@@ -23,7 +23,7 @@ solvers
         nAlphaSubCycles 2;
     }
 
-    p
+    p_rgh
     {
         solver          GAMG;
         smoother        DIC;
@@ -38,9 +38,9 @@ solvers
         relTol          0.01;
     }
 
-    pFinal
+    p_rghFinal
     {
-        $p;
+        $p_rgh;
         relTol          0;
     }
 

tutorials/multiphase/twoPhaseEulerFoam/laminar/bubbleColumnIATE/0/p

@@ -22,17 +22,17 @@ boundaryField
 {
     inlet
     {
-        type               fixedFluxPressure;
+        type               calculated;
         value              $internalField;
     }
     outlet
     {
-        type               fixedValue;
+        type               calculated;
         value              $internalField;
     }
     walls
     {
-        type               fixedFluxPressure;
+        type               calculated;
         value              $internalField;
     }
 }