incompressible/pimpleDyMFoam, solver + tutorials

applications/solvers/incompressible/pimpleDyMFoam/UEqn.H

@@ -1,27 +1,33 @@
-    fvVectorMatrix UEqn
+    // Convection-diffusion matrix
+    fvVectorMatrix HUEqn
     (
-        fvm::ddt(U)
+        fvm::div(phi, U)
-      + fvm::div(phi, U)
       + turbulence->divDevReff(U)
     );
 
+    // Time derivative matrix
+    fvVectorMatrix ddtUEqn(fvm::ddt(U));
+
+    // Get under-relaxation factor
+    scalar UUrf = mesh.solutionDict().relaxationFactor(U.name());
+
     if (oCorr == nOuterCorr - 1)
     {
         if (mesh.solutionDict().relax("UFinal"))
         {
-            UEqn.relax(mesh.solutionDict().relaxationFactor("UFinal"));
+            UUrf = mesh.solutionDict().relaxationFactor("UFinal");
         }
         else
         {
-            UEqn.relax(1);
+            UUrf = 1;
         }
     }
-    else
-    {
-        UEqn.relax();
-    }
 
-    if (momentumPredictor)
+    // Solve momentum predictor
-    {
+    solve
-        solve(UEqn == -fvc::grad(p));
+    (
-    }
+        ddtUEqn
+      + relax(HUEqn, UUrf)
+     ==
+      - fvc::grad(p)
+    );

applications/solvers/incompressible/pimpleDyMFoam/correctPhi.H

@@ -39,7 +39,7 @@
     {
         fvScalarMatrix pcorrEqn
         (
-            fvm::laplacian(rAU, pcorr) == fvc::div(phi)
+            fvm::laplacian(1/aU, pcorr) == fvc::div(phi)
         );
 
         pcorrEqn.setReference(pRefCell, pRefValue);

applications/solvers/incompressible/pimpleDyMFoam/createFields.H

@@ -41,18 +41,18 @@
         incompressible::turbulenceModel::New(U, phi, laminarTransport)
     );
 
-    Info<< "Reading field rAU if present\n" << endl;
+    Info<< "Reading field aU if present\n" << endl;
-    volScalarField rAU
+    volScalarField aU
     (
         IOobject
         (
-            "rAU",
+            "aU",
             runTime.timeName(),
             mesh,
             IOobject::READ_IF_PRESENT,
             IOobject::AUTO_WRITE
         ),
         mesh,
-        runTime.deltaT(),
+        1/runTime.deltaT(),
         zeroGradientFvPatchScalarField::typeName
     );

applications/solvers/incompressible/pimpleDyMFoam/pEqn.H

@@ -0,0 +1,70 @@
+{
+    p.boundaryField().updateCoeffs();
+
+    // Prepare clean Ap without time derivative contribution and
+    // without contribution from under-relaxation
+    // HJ, 26/Oct/2015
+    aU = HUEqn.A();
+
+    // Store velocity under-relaxation point before using U for
+    // the flux precursor
+    U.storePrevIter();
+
+    U = HUEqn.H()/aU;
+    phi = (fvc::interpolate(U) & mesh.Sf());
+
+    // Global flux balance
+    adjustPhi(phi, U, p);
+
+    for (int nonOrth = 0; nonOrth <= nNonOrthCorr; nonOrth++)
+    {
+        fvScalarMatrix pEqn
+        (
+            fvm::laplacian(1/aU, p) == fvc::div(phi)
+        );
+
+        pEqn.setReference(pRefCell, pRefValue);
+
+        if
+        (
+            corr == nCorr - 1
+         && nonOrth == nNonOrthCorr
+        )
+        {
+            pEqn.solve
+            (
+                mesh.solutionDict().solver(p.name() + "Final")
+            );
+        }
+        else
+        {
+            pEqn.solve(mesh.solutionDict().solver(p.name()));
+        }
+
+        if (nonOrth == nNonOrthCorr)
+        {
+            phi -= pEqn.flux();
+        }
+    }
+
+    // Explicitly relax pressure for momentum corrector
+    if (oCorr != nOuterCorr - 1)
+    {
+        p.relax();
+    }
+
+    // Make the fluxes relative to the mesh motion
+    fvc::makeRelative(phi, U);
+
+#   include "movingMeshContinuityErrs.H"
+
+    U = UUrf*
+        (
+            1.0/(aU + ddtUEqn.A())*
+            (
+                U*aU - fvc::grad(p) + ddtUEqn.H()
+            )
+        )
+      + (1 - UUrf)*U.prevIter();
+    U.correctBoundaryConditions();
+}

applications/solvers/incompressible/pimpleDyMFoam/pimpleDyMFoam.C

@@ -30,6 +30,11 @@ Description
 
     Turbulence modelling is generic, i.e. laminar, RAS or LES may be selected.
 
+    Consistent formulation without time-step and relaxation dependence by Jasak
+
+Author
+    Hrvoje Jasak, Wikki Ltd.  All rights reserved
+
 \*---------------------------------------------------------------------------*/
 
 #include "fvCFD.H"
@@ -106,61 +111,7 @@ int main(int argc, char *argv[])
             // --- PISO loop
             for (int corr = 0; corr < nCorr; corr++)
             {
-                rAU = 1.0/UEqn.A();
+#               include "pEqn.H"
-
-                U = rAU*UEqn.H();
-                phi = (fvc::interpolate(U) & mesh.Sf());
-                // ddtPhiCorr does not work.  HJ, 20/Nov/2013
-
-                adjustPhi(phi, U, p);
-
-                for (int nonOrth=0; nonOrth<=nNonOrthCorr; nonOrth++)
-                {
-                    fvScalarMatrix pEqn
-                    (
-                        fvm::laplacian(rAU, p) == fvc::div(phi)
-                    );
-
-                    pEqn.setReference(pRefCell, pRefValue);
-
-                    if
-                    (
-//                         oCorr == nOuterCorr - 1
-                        corr == nCorr - 1
-                     && nonOrth == nNonOrthCorr
-                    )
-                    {
-                        pEqn.solve
-                        (
-                            mesh.solutionDict().solver(p.name() + "Final")
-                        );
-                    }
-                    else
-                    {
-                        pEqn.solve(mesh.solutionDict().solver(p.name()));
-                    }
-
-                    if (nonOrth == nNonOrthCorr)
-                    {
-                        phi -= pEqn.flux();
-                    }
-                }
-
-#               include "continuityErrs.H"
-
-                // Explicitly relax pressure for momentum corrector
-                if (oCorr != nOuterCorr - 1)
-                {
-                    p.relax();
-                }
-
-                // Make the fluxes relative to the mesh motion
-                fvc::makeRelative(phi, U);
-
-#               include "movingMeshContinuityErrs.H"
-
-                U -= rAU*fvc::grad(p);
-                U.correctBoundaryConditions();
             }
 
             turbulence->correct();

tutorials/incompressible/pimpleDyMFoam/movingCone/system/fvSchemes

@@ -29,7 +29,7 @@ gradSchemes
 divSchemes
 {
     default         none;
-    div(phi,U)      Gauss linear;
+    div(phi,U)      Gauss linearUpwind Gauss linear;
     div((nuEff*dev(grad(U).T()))) Gauss linear;
 }
 
@@ -37,8 +37,8 @@ laplacianSchemes
 {
     default         none;
     laplacian(nu,U) Gauss linear corrected;
-    laplacian(rAU,pcorr) Gauss linear corrected;
+    laplacian((1|aU),pcorr) Gauss linear corrected;
-    laplacian(rAU,p) Gauss linear corrected;
+    laplacian((1|aU),p)  Gauss linear corrected;
     laplacian(diffusivity,cellMotionU) Gauss linear uncorrected;
     laplacian(nuEff,U) Gauss linear uncorrected;
 }

tutorials/incompressible/pimpleDyMFoam/movingCone/system/fvSolution

@@ -65,4 +65,10 @@ PIMPLE
     nNonOrthogonalCorrectors 0;
 }
 
+relaxationFactors
+{
+    U               1;
+    UFinal          1;
+}
+
 // ************************************************************************* //

tutorials/incompressible/pimpleDyMFoam/movingCylinders/system/fvSchemes

@@ -41,14 +41,15 @@ laplacianSchemes
 
     laplacian(1,p) Gauss linear limited 0.5;
 
-    laplacian((1|A(U)),p) Gauss linear limited 0.5;
+    laplacian((1|aU),pcorr) Gauss linear limited 0.5;
+    laplacian((1|aU),p) Gauss linear limited 0.5;
 }
 
 interpolationSchemes
 {
     default         linear;
     interpolate(HbyA) linear;
-    interpolate(1|A) linear;
+    interpolate(1|aU) linear;
 }
 
 snGradSchemes