INT: Integration of isoAdvector and supporting material

Community contribution from Johan Roenby, DHI

IsoAdvector is a geometric Volume-of-Fluid method for advection of a
sharp interface between two incompressible fluids. It works on both
structured and unstructured meshes with no requirements on cell shapes.
IsoAdvector is as an alternative choice for the interface compression
treatment with the MULES limiter implemented in the interFoam family
of solvers.

The isoAdvector concept and code was developed at DHI and was funded
by a Sapere Aude postdoc grant to Johan Roenby from The Danish Council
for Independent Research | Technology and Production Sciences (Grant-ID:
DFF - 1337-00118B - FTP).
Co-funding is also provided by the GTS grant to DHI from the Danish
Agency for Science, Technology and Innovation.

The ideas behind and performance of the isoAdvector scheme is
documented in:

    Roenby J, Bredmose H, Jasak H. 2016 A computational method for sharp
    interface  advection. R. Soc. open sci. 3: 160405.
    [http://dx.doi.org/10.1098/rsos.160405](http://dx.doi.org/10.1098/rsos.160405)

Videos showing isoAdvector's performance with a number of standard
test cases can be found in this youtube channel:

    https://www.youtube.com/channel/UCt6Idpv4C8TTgz1iUX0prAA

Project contributors:

* Johan Roenby <jro@dhigroup.com> (Inventor and main developer)
* Hrvoje Jasak <hrvoje.jasak@fsb.hr> (Consistent treatment of
  boundary faces including processor boundaries, parallelisation,
  code clean up
* Henrik Bredmose <hbre@dtu.dk> (Assisted in the conceptual
  development)
* Vuko Vukcevic <vuko.vukcevic@fsb.hr> (Code review, profiling,
  porting to foam-extend, bug fixing, testing)
* Tomislav Maric <tomislav@sourceflux.de> (Source file
  rearrangement)
* Andy Heather <a.heather@opencfd.co.uk> (Integration into OpenFOAM
  for v1706 release)

See the integration repository below to see the full set of changes
implemented for release into OpenFOAM v1706

    https://develop.openfoam.com/Community/Integration-isoAdvector

applications/solvers/multiphase/interIsoFoam/Make/files

@@ -0,0 +1,3 @@
+interIsoFoam.C
+
+EXE = $(FOAM_APPBIN)/interIsoFoam

applications/solvers/multiphase/interIsoFoam/Make/options

@@ -0,0 +1,20 @@
+EXE_INC = \
+    -I$(LIB_SRC)/transportModels/twoPhaseMixture/lnInclude \
+    -I$(LIB_SRC)/transportModels \
+    -I$(LIB_SRC)/transportModels/incompressible/lnInclude \
+    -I$(LIB_SRC)/transportModels/interfaceProperties/lnInclude \
+    -I$(LIB_SRC)/TurbulenceModels/turbulenceModels/lnInclude \
+    -I$(LIB_SRC)/TurbulenceModels/incompressible/lnInclude \
+    -I$(LIB_SRC)/transportModels/immiscibleIncompressibleTwoPhaseMixture/lnInclude \
+    -I$(LIB_SRC)/finiteVolume/lnInclude \
+    -I$(LIB_SRC)/meshTools/lnInclude \
+    -I$(LIB_SRC)/sampling/lnInclude
+
+EXE_LIBS = \
+    -limmiscibleIncompressibleTwoPhaseMixture \
+    -lturbulenceModels \
+    -lincompressibleTurbulenceModels \
+    -lfiniteVolume \
+    -lfvOptions \
+    -lmeshTools \
+    -lsampling

applications/solvers/multiphase/interIsoFoam/UEqn.H

@@ -0,0 +1,33 @@
+    MRF.correctBoundaryVelocity(U);
+
+    fvVectorMatrix UEqn
+    (
+        fvm::ddt(rho, U) + fvm::div(rhoPhi, U)
+      + MRF.DDt(rho, U)
+      + turbulence->divDevRhoReff(rho, U)
+     ==
+        fvOptions(rho, U)
+    );
+
+    UEqn.relax();
+
+    fvOptions.constrain(UEqn);
+
+    if (pimple.momentumPredictor())
+    {
+        solve
+        (
+            UEqn
+         ==
+            fvc::reconstruct
+            (
+                (
+                    mixture.surfaceTensionForce()
+                  - ghf*fvc::snGrad(rho)
+                  - fvc::snGrad(p_rgh)
+                ) * mesh.magSf()
+            )
+        );
+
+        fvOptions.correct(U);
+    }

applications/solvers/multiphase/interIsoFoam/alphaControls.H

@@ -0,0 +1,4 @@
+const dictionary& alphaControls = mesh.solverDict(alpha1.name());
+
+label nAlphaSubCycles(readLabel(alphaControls.lookup("nAlphaSubCycles")));
+

applications/solvers/multiphase/interIsoFoam/alphaCourantNo.H

@@ -0,0 +1,57 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2011-2016 OpenFOAM Foundation
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Global
+    alphaCourantNo
+
+Description
+    Calculates and outputs the mean and maximum Courant Numbers.
+
+\*---------------------------------------------------------------------------*/
+
+scalar maxAlphaCo
+(
+    readScalar(runTime.controlDict().lookup("maxAlphaCo"))
+);
+
+scalar alphaCoNum = 0.0;
+scalar meanAlphaCoNum = 0.0;
+
+if (mesh.nInternalFaces())
+{
+    scalarField sumPhi
+    (
+        mixture.nearInterface()().primitiveField()
+       *fvc::surfaceSum(mag(phi))().primitiveField()
+    );
+
+    alphaCoNum = 0.5*gMax(sumPhi/mesh.V().field())*runTime.deltaTValue();
+
+    meanAlphaCoNum =
+        0.5*(gSum(sumPhi)/gSum(mesh.V().field()))*runTime.deltaTValue();
+}
+
+Info<< "Interface Courant Number mean: " << meanAlphaCoNum
+    << " max: " << alphaCoNum << endl;
+
+// ************************************************************************* //

applications/solvers/multiphase/interIsoFoam/alphaEqn.H

@@ -0,0 +1,35 @@
+// If there are more than one outer corrector, we use a mixture of old and
+// new U and phi for propagating alpha1 in all but the first outer iteration
+if (!pimple.firstIter())
+{
+    // We are recalculating alpha1 from the its old time value
+    alpha1 = alpha1.oldTime();
+    // Temporarily storing new U and phi values in prevIter storage
+    U.storePrevIter();
+    phi.storePrevIter();
+
+    // Overwriting new U and phi values with mixture of old and new values
+    phi = 0.5*(phi + phi.oldTime());
+    U = 0.5*(U + U.oldTime());
+}
+
+// Update alpha1
+advector.advect();
+
+// Update rhoPhi
+rhoPhi = advector.getRhoPhi(rho1, rho2);
+
+alpha2 = 1.0 - alpha1;
+
+if (!pimple.firstIter())
+{
+    // Restoring new U and phi values temporarily saved in prevIter() above
+    U = U.prevIter();
+    phi = phi.prevIter();
+}
+
+Info<< "Phase-1 volume fraction = "
+    << alpha1.weightedAverage(mesh.Vsc()).value()
+    << "  Min(" << alpha1.name() << ") = " << min(alpha1).value()
+    << "  Max(" << alpha1.name() << ") - 1 = " << max(alpha1).value() - 1
+    << endl;

applications/solvers/multiphase/interIsoFoam/alphaEqnSubCycle.H

@@ -0,0 +1,35 @@
+if (nAlphaSubCycles > 1)
+{
+    dimensionedScalar totalDeltaT = runTime.deltaT();
+    surfaceScalarField rhoPhiSum
+    (
+        IOobject
+        (
+            "rhoPhiSum",
+            runTime.timeName(),
+            mesh
+        ),
+        mesh,
+        dimensionedScalar("0", rhoPhi.dimensions(), 0)
+    );
+
+    tmp<volScalarField> trSubDeltaT;
+
+    for
+    (
+        subCycle<volScalarField> alphaSubCycle(alpha1, nAlphaSubCycles);
+        !(++alphaSubCycle).end();
+    )
+    {
+        #include "alphaEqn.H"
+        rhoPhiSum += (runTime.deltaT()/totalDeltaT)*rhoPhi;
+    }
+
+    rhoPhi = rhoPhiSum;
+}
+else
+{
+    #include "alphaEqn.H"
+}
+
+rho == alpha1*rho1 + alpha2*rho2;

applications/solvers/multiphase/interIsoFoam/correctPhi.H

@@ -0,0 +1,11 @@
+CorrectPhi
+(
+    U,
+    phi,
+    p_rgh,
+    dimensionedScalar("rAUf", dimTime/rho.dimensions(), 1),
+    geometricZeroField(),
+    pimple
+);
+
+#include "continuityErrs.H"

applications/solvers/multiphase/interIsoFoam/createFields.H

@@ -0,0 +1,123 @@
+Info<< "Reading field p_rgh\n" << endl;
+volScalarField p_rgh
+(
+    IOobject
+    (
+        "p_rgh",
+        runTime.timeName(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::AUTO_WRITE
+    ),
+    mesh
+);
+
+Info<< "Reading field U\n" << endl;
+volVectorField U
+(
+    IOobject
+    (
+        "U",
+        runTime.timeName(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::AUTO_WRITE
+    ),
+    mesh
+);
+
+#include "createPhi.H"
+
+
+Info<< "Reading transportProperties\n" << endl;
+immiscibleIncompressibleTwoPhaseMixture mixture(U, phi);
+
+volScalarField& alpha1(mixture.alpha1());
+volScalarField& alpha2(mixture.alpha2());
+
+const dimensionedScalar& rho1 = mixture.rho1();
+const dimensionedScalar& rho2 = mixture.rho2();
+
+
+// Need to store rho for ddt(rho, U)
+volScalarField rho
+(
+    IOobject
+    (
+        "rho",
+        runTime.timeName(),
+        mesh,
+        IOobject::READ_IF_PRESENT
+    ),
+    alpha1*rho1 + alpha2*rho2
+);
+rho.oldTime();
+
+
+// Mass flux
+surfaceScalarField rhoPhi
+(
+    IOobject
+    (
+        "rhoPhi",
+        runTime.timeName(),
+        mesh,
+        IOobject::NO_READ,
+        IOobject::NO_WRITE
+    ),
+    fvc::interpolate(rho)*phi
+);
+
+
+// Construct incompressible turbulence model
+autoPtr<incompressible::turbulenceModel> turbulence
+(
+    incompressible::turbulenceModel::New(U, phi, mixture)
+);
+
+
+#include "readGravitationalAcceleration.H"
+#include "readhRef.H"
+#include "gh.H"
+
+
+volScalarField p
+(
+    IOobject
+    (
+        "p",
+        runTime.timeName(),
+        mesh,
+        IOobject::NO_READ,
+        IOobject::AUTO_WRITE
+    ),
+    p_rgh + rho*gh
+);
+
+label pRefCell = 0;
+scalar pRefValue = 0.0;
+setRefCell
+(
+    p,
+    p_rgh,
+    pimple.dict(),
+    pRefCell,
+    pRefValue
+);
+
+if (p_rgh.needReference())
+{
+    p += dimensionedScalar
+    (
+        "p",
+        p.dimensions(),
+        pRefValue - getRefCellValue(p, pRefCell)
+    );
+    p_rgh = p - rho*gh;
+}
+
+mesh.setFluxRequired(p_rgh.name());
+mesh.setFluxRequired(alpha1.name());
+
+#include "createMRF.H"
+#include "createIsoAdvection.H"

applications/solvers/multiphase/interIsoFoam/createIsoAdvection.H

@@ -0,0 +1,10 @@
+// Defining isoAdvection
+isoAdvection advector(alpha1, phi, U);
+
+bool frozenFlow = pimple.dict().lookupOrDefault<bool>("frozenFlow", false);
+if (frozenFlow)
+{
+    Info<< "Employing frozen-flow assumption: "
+        << "pressure-velocity system will not be updated"
+        << endl;
+}

applications/solvers/multiphase/interIsoFoam/interIsoFoam.C

@@ -0,0 +1,143 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2011-2017 OpenFOAM Foundation
+     \\/     M anipulation  | Copyright (C) 2017 OpenCFD Ltd.
+-------------------------------------------------------------------------------
+                isoAdvector | Copyright (C) 2016 DHI
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Application
+    interIsoFoam
+
+Group
+    grpMultiphaseSolvers
+
+Description
+    Solver derived from interFoam for 2 incompressible, isothermal immiscible
+    fluids using the iso-advector phase-fraction based interface capturing
+    approach.
+
+    The momentum and other fluid properties are of the "mixture" and a single
+    momentum equation is solved.
+
+    Turbulence modelling is generic, i.e. laminar, RAS or LES may be selected.
+
+    For a two-fluid approach see twoPhaseEulerFoam.
+
+    Reference:
+        \verbatim
+            Roenby, J., Bredmose, H. and Jasak, H. (2016).
+            A computational method for sharp interface advection
+            Royal Society Open Science, 3
+            doi 10.1098/rsos.160405
+        \endverbatim
+
+    isoAdvector code supplied by Johan Roenby, DHI (2016)
+
+\*---------------------------------------------------------------------------*/
+
+#include "isoAdvection.H"
+#include "fvCFD.H"
+#include "subCycle.H"
+#include "immiscibleIncompressibleTwoPhaseMixture.H"
+#include "turbulentTransportModel.H"
+#include "pimpleControl.H"
+#include "fvOptions.H"
+#include "CorrectPhi.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+int main(int argc, char *argv[])
+{
+    #include "postProcess.H"
+
+    #include "setRootCase.H"
+    #include "createTime.H"
+    #include "createMesh.H"
+    #include "createControl.H"
+    #include "createTimeControls.H"
+    #include "initContinuityErrs.H"
+    #include "createFields.H"
+    #include "createFvOptions.H"
+    #include "correctPhi.H"
+
+    turbulence->validate();
+
+    #include "readTimeControls.H"
+    #include "CourantNo.H"
+    #include "setInitialDeltaT.H"
+
+    // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+    Info<< "\nStarting time loop\n" << endl;
+
+    while (runTime.run())
+    {
+        #include "readTimeControls.H"
+
+        #include "CourantNo.H"
+        #include "alphaCourantNo.H"
+        #include "setDeltaT.H"
+
+        runTime++;
+
+        Info<< "Time = " << runTime.timeName() << nl << endl;
+
+        // --- Pressure-velocity PIMPLE corrector loop
+        while (pimple.loop())
+        {
+            #include "alphaControls.H"
+            #include "alphaEqnSubCycle.H"
+
+            mixture.correct();
+
+            if (frozenFlow)
+            {
+                continue;
+            }
+
+            #include "UEqn.H"
+
+            // --- Pressure corrector loop
+            while (pimple.correct())
+            {
+                #include "pEqn.H"
+            }
+
+            if (pimple.turbCorr())
+            {
+                turbulence->correct();
+            }
+        }
+
+        runTime.write();
+
+        Info<< "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
+            << "  ClockTime = " << runTime.elapsedClockTime() << " s"
+            << nl << endl;
+    }
+
+    Info<< "End\n" << endl;
+
+    return 0;
+}
+
+
+// ************************************************************************* //

applications/solvers/multiphase/interIsoFoam/pEqn.H

@@ -0,0 +1,67 @@
+{
+    volScalarField rAU("rAU", 1.0/UEqn.A());
+    surfaceScalarField rAUf("rAUf", fvc::interpolate(rAU));
+
+    volVectorField HbyA(constrainHbyA(rAU*UEqn.H(), U, p_rgh));
+
+    surfaceScalarField phiHbyA
+    (
+        "phiHbyA",
+        fvc::flux(HbyA)
+      + fvc::interpolate(rho*rAU)*fvc::ddtCorr(U, phi)
+    );
+    MRF.makeRelative(phiHbyA);
+    adjustPhi(phiHbyA, U, p_rgh);
+
+    surfaceScalarField phig
+    (
+        (
+            mixture.surfaceTensionForce()
+          - ghf*fvc::snGrad(rho)
+        )*rAUf*mesh.magSf()
+//          - ghf*(fvc::grad(rho) & mesh.Sf())*rAUf
+    );
+
+    phiHbyA += phig;
+
+    // Update the pressure BCs to ensure flux consistency
+    constrainPressure(p_rgh, U, phiHbyA, rAUf, MRF);
+
+    while (pimple.correctNonOrthogonal())
+    {
+        fvScalarMatrix p_rghEqn
+        (
+            fvm::laplacian(rAUf, p_rgh) == fvc::div(phiHbyA)
+        );
+
+        p_rghEqn.setReference(pRefCell, getRefCellValue(p_rgh, pRefCell));
+
+        p_rghEqn.solve(mesh.solver(p_rgh.select(pimple.finalInnerIter())));
+
+        if (pimple.finalNonOrthogonalIter())
+        {
+            phi = phiHbyA - p_rghEqn.flux();
+
+            p_rgh.relax();
+
+            U = HbyA + rAU*fvc::reconstruct((phig - p_rghEqn.flux())/rAUf);
+            U.correctBoundaryConditions();
+            fvOptions.correct(U);
+        }
+    }
+
+    #include "continuityErrs.H"
+
+    p == p_rgh + rho*gh;
+
+    if (p_rgh.needReference())
+    {
+        p += dimensionedScalar
+        (
+            "p",
+            p.dimensions(),
+            pRefValue - getRefCellValue(p, pRefCell)
+        );
+        p_rgh = p - rho*gh;
+    }
+}

applications/solvers/multiphase/interIsoFoam/setDeltaT.H

@@ -0,0 +1,53 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2011 OpenFOAM Foundation
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Global
+    setDeltaT
+
+Description
+    Reset the timestep to maintain a constant maximum courant Number.
+    Reduction of time-step is immediate, but increase is damped to avoid
+    unstable oscillations.
+
+\*---------------------------------------------------------------------------*/
+
+if (adjustTimeStep)
+{
+    scalar maxDeltaTFact =
+        min(maxCo/(CoNum + SMALL), maxAlphaCo/(alphaCoNum + SMALL));
+
+    scalar deltaTFact = min(min(maxDeltaTFact, 1.0 + 0.1*maxDeltaTFact), 1.2);
+
+    runTime.setDeltaT
+    (
+        min
+        (
+            deltaTFact*runTime.deltaTValue(),
+            maxDeltaT
+        )
+    );
+
+    Info<< "deltaT = " <<  runTime.deltaTValue() << endl;
+}
+
+// ************************************************************************* //