Initial commit

OpenFOAM-v2112/applications/solvers/finiteArea/surfactantFoam/Make/options

+EXE_INC = \
+    -I$(LIB_SRC)/finiteArea/lnInclude \
+    -I$(LIB_SRC)/finiteVolume/lnInclude \
+    -I$(LIB_SRC)/meshTools/lnInclude \
+    -I$(LIB_SRC)/cfdTools/general/lnInclude
+
+EXE_LIBS = \
+    -lfiniteArea \
+    -lfiniteVolume \
+    -lmeshTools

OpenFOAM-v2112/applications/solvers/finiteArea/surfactantFoam/createFaFields.H

+Info<< "Reading field Cs" << endl;
+areaScalarField Cs
+(
+    IOobject
+    (
+        "Cs",
+        runTime.timeName(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::AUTO_WRITE
+    ),
+    aMesh
+);
+
+Info<< "Reading transportProperties\n" << endl;
+
+IOdictionary transportProperties
+(
+    IOobject
+    (
+        "transportProperties",
+        runTime.constant(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::NO_WRITE
+    )
+);
+
+
+Info<< "Reading diffusivity D\n" << endl;
+
+dimensionedScalar Ds("Ds", dimViscosity, transportProperties);
+
+areaVectorField Us
+(
+    IOobject
+    (
+        "Us",
+        runTime.timeName(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::NO_WRITE
+    ),
+    aMesh
+);
+
+
+edgeScalarField phis
+(
+    IOobject
+    (
+        "phis",
+        runTime.timeName(),
+        mesh,
+        IOobject::NO_READ,
+        IOobject::NO_WRITE
+    ),
+    linearEdgeInterpolate(Us) & aMesh.Le()
+);

OpenFOAM-v2112/applications/solvers/finiteArea/surfactantFoam/createFaMesh.H

+    // Create Finite Area mesh
+    faMesh aMesh(mesh);

OpenFOAM-v2112/applications/solvers/finiteArea/surfactantFoam/createVolFields.H

+    // Create volume-to surface mapping object
+    volSurfaceMapping vsm(aMesh);
+
+    volScalarField Cvf
+    (
+        IOobject
+        (
+            "Cvf",
+            runTime.timeName(),
+            mesh,
+            IOobject::NO_READ,
+            IOobject::AUTO_WRITE
+        ),
+        mesh,
+        dimensionedScalar(dimless/dimLength, Zero)
+    );
+
+    vsm.mapToVolume(Cs, Cvf.boundaryFieldRef());
+    //Cvf.write();
+
+    volVectorField U
+    (
+        IOobject
+        (
+            "U",
+            runTime.timeName(),
+            mesh,
+            IOobject::NO_READ,
+            IOobject::AUTO_WRITE
+        ),
+        mesh,
+        dimensionedVector(dimVelocity, Zero)
+    );
+
+    vsm.mapToVolume(Us, U.boundaryFieldRef());
+    //U.write();

OpenFOAM-v2112/applications/solvers/finiteArea/surfactantFoam/surfactantFoam.C

+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2016-2017 Wikki Ltd
+-------------------------------------------------------------------------------
+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
+    surfactantFoam
+
+Group
+    grpFiniteAreaSolvers
+
+Description
+    Passive scalar transport finiteArea equation solver.
+
+    \heading Solver details
+    The equation is given by:
+
+    \f[
+        \ddt{Cs} + \div \left(\vec{U} Cs\right) - \div \left(D_T \grad Cs \right)
+        = 0
+    \f]
+
+    Where:
+    \vartable
+        Cs      | Passive scalar
+        Ds      | Diffusion coefficient
+    \endvartable
+
+    \heading Required fields
+    \plaintable
+        Cs      | Passive scalar
+        Us      | Velocity [m/s]
+    \endplaintable
+
+Author
+    Zeljko Tukovic, FMENA
+    Hrvoje Jasak, Wikki Ltd.
+
+\*---------------------------------------------------------------------------*/
+
+#include "fvCFD.H"
+#include "faCFD.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+int main(int argc, char *argv[])
+{
+    argList::addNote
+    (
+        "Passive scalar transport finiteArea equation solver."
+    );
+
+    #include "setRootCaseLists.H"
+    #include "createTime.H"
+    #include "createMesh.H"
+    #include "createFaMesh.H"
+    #include "createFaFields.H"
+    #include "createVolFields.H"
+
+    Info<< "Total mass of surfactant: "
+        << sum(Cs.internalField()*aMesh.S()) << endl;
+
+    Info<< "\nStarting time loop\n" << endl;
+
+    while (runTime.loop())
+    {
+        Info<< "Time = " << runTime.value() << endl;
+
+        faScalarMatrix CsEqn
+        (
+            fam::ddt(Cs)
+          + fam::div(phis, Cs)
+          - fam::laplacian(Ds, Cs)
+        );
+
+        CsEqn.solve();
+
+        if (runTime.writeTime())
+        {
+            vsm.mapToVolume(Cs, Cvf.boundaryFieldRef());
+
+            runTime.write();
+        }
+
+        Info<< "Total mass of surfactant: "
+            << sum(Cs.internalField()*aMesh.S()) << endl;
+
+        runTime.printExecutionTime(Info);
+    }
+
+    Info<< "End\n" << endl;
+
+    return 0;
+}
+
+
+// ************************************************************************* //

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqPimpleFoam/Make/files

+buoyantBoussinesqPimpleFoam.C
+
+EXE = $(FOAM_APPBIN)/buoyantBoussinesqPimpleFoam

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqPimpleFoam/Make/options

+EXE_INC = \
+    -I../buoyantBoussinesqSimpleFoam \
+    -I../../incompressible/pimpleFoam \
+    -I$(LIB_SRC)/sampling/lnInclude \
+    -I$(LIB_SRC)/finiteVolume/lnInclude \
+    -I$(LIB_SRC)/meshTools/lnInclude \
+    -I$(LIB_SRC)/dynamicMesh/lnInclude \
+    -I$(LIB_SRC)/dynamicFvMesh/lnInclude \
+    -I$(LIB_SRC)/TurbulenceModels/turbulenceModels/lnInclude \
+    -I$(LIB_SRC)/TurbulenceModels/incompressible/lnInclude \
+    -I$(LIB_SRC)/transportModels \
+    -I$(LIB_SRC)/transportModels/incompressible/singlePhaseTransportModel \
+    -I$(LIB_SRC)/thermophysicalModels/radiation/lnInclude
+
+EXE_LIBS = \
+    -lfiniteVolume \
+    -lfvOptions \
+    -lmeshTools \
+    -ldynamicMesh \
+    -ldynamicFvMesh \
+    -lsampling \
+    -lturbulenceModels \
+    -lincompressibleTurbulenceModels \
+    -lincompressibleTransportModels \
+    -lradiationModels \
+    -latmosphericModels

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqPimpleFoam/TEqn.H

+{
+    alphat = turbulence->nut()/Prt;
+    alphat.correctBoundaryConditions();
+
+    volScalarField alphaEff("alphaEff", turbulence->nu()/Pr + alphat);
+
+    fvScalarMatrix TEqn
+    (
+        fvm::ddt(T)
+      + fvm::div(phi, T)
+      - fvm::laplacian(alphaEff, T)
+     ==
+        radiation->ST(rhoCpRef, T)
+      + fvOptions(T)
+    );
+
+    TEqn.relax();
+
+    fvOptions.constrain(TEqn);
+
+    TEqn.solve();
+
+    radiation->correct();
+
+    fvOptions.correct(T);
+
+    rhok = 1.0 - beta*(T - TRef);
+}

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqPimpleFoam/UEqn.H

+    // Solve the momentum equation
+
+    MRF.correctBoundaryVelocity(U);
+
+    fvVectorMatrix UEqn
+    (
+        fvm::ddt(U) + fvm::div(phi, U)
+      + MRF.DDt(U)
+      + turbulence->divDevReff(U)
+     ==
+        fvOptions(U)
+    );
+
+    UEqn.relax();
+
+    fvOptions.constrain(UEqn);
+
+    if (pimple.momentumPredictor())
+    {
+        solve
+        (
+            UEqn
+         ==
+            fvc::reconstruct
+            (
+                (
+                  - ghf*fvc::snGrad(rhok)
+                  - fvc::snGrad(p_rgh)
+                )*mesh.magSf()
+            )
+        );
+
+        fvOptions.correct(U);
+    }

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqPimpleFoam/buoyantBoussinesqPimpleFoam.C

+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2011-2017 OpenFOAM Foundation
+    Copyright (C) 2021 OpenCFD Ltd.
+-------------------------------------------------------------------------------
+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
+    buoyantBoussinesqPimpleFoam
+
+Group
+    grpHeatTransferSolvers
+
+Description
+    Transient solver for buoyant, turbulent flow of incompressible fluids,
+    with optional mesh motion and mesh topology changes.
+
+    Uses the Boussinesq approximation:
+    \f[
+        rho_{k} = 1 - beta(T - T_{ref})
+    \f]
+
+    where:
+        \f$ rho_{k} \f$ = the effective (driving) kinematic density
+        beta = thermal expansion coefficient [1/K]
+        T = temperature [K]
+        \f$ T_{ref} \f$ = reference temperature [K]
+
+    Valid when:
+    \f[
+        \frac{beta(T - T_{ref})}{rho_{ref}} << 1
+    \f]
+
+\*---------------------------------------------------------------------------*/
+
+#include "fvCFD.H"
+#include "dynamicFvMesh.H"
+#include "singlePhaseTransportModel.H"
+#include "turbulentTransportModel.H"
+#include "radiationModel.H"
+#include "CorrectPhi.H"
+#include "fvOptions.H"
+#include "pimpleControl.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+int main(int argc, char *argv[])
+{
+    argList::addNote
+    (
+        "Transient solver for buoyant, turbulent flow"
+        " of incompressible fluids, with optional mesh"
+        " motion and mesh topology changes.\n"
+        "Uses the Boussinesq approximation."
+    );
+
+    #include "postProcess.H"
+
+    #include "addCheckCaseOptions.H"
+    #include "setRootCaseLists.H"
+    #include "createTime.H"
+    #include "createDynamicFvMesh.H"
+    #include "createDyMControls.H"
+    #include "createFields.H"
+    #include "createUfIfPresent.H"
+    #include "CourantNo.H"
+    #include "setInitialDeltaT.H"
+    #include "initContinuityErrs.H"
+
+    turbulence->validate();
+
+    // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+    Info<< "\nStarting time loop\n" << endl;
+
+    while (runTime.run())
+    {
+        #include "readDyMControls.H"
+        #include "CourantNo.H"
+        #include "setDeltaT.H"
+
+        ++runTime;
+
+        Info<< "Time = " << runTime.timeName() << nl << endl;
+
+        // --- Pressure-velocity PIMPLE corrector loop
+        while (pimple.loop())
+        {
+            if (pimple.firstIter() || moveMeshOuterCorrectors)
+            {
+                // Do any mesh changes
+                mesh.controlledUpdate();
+
+                if (mesh.changing())
+                {
+                    MRF.update();
+
+                    if (correctPhi)
+                    {
+                        // Calculate absolute flux
+                        // from the mapped surface velocity
+                        phi = mesh.Sf() & Uf();
+
+                        #include "correctPhi.H"
+
+                        // Make the flux relative to the mesh motion
+                        fvc::makeRelative(phi, U);
+                    }
+
+                    if (checkMeshCourantNo)
+                    {
+                        #include "meshCourantNo.H"
+                    }
+                }
+            }
+
+            #include "UEqn.H"
+            #include "TEqn.H"
+
+            // --- Pressure corrector loop
+            while (pimple.correct())
+            {
+                #include "pEqn.H"
+            }
+
+            if (pimple.turbCorr())
+            {
+                laminarTransport.correct();
+                turbulence->correct();
+            }
+        }
+
+        runTime.write();
+
+        runTime.printExecutionTime(Info);
+    }
+
+    Info<< "End\n" << endl;
+
+    return 0;
+}
+
+
+// ************************************************************************* //

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqPimpleFoam/createFields.H

+Info<< "Reading thermophysical properties\n" << endl;
+
+Info<< "Reading field T\n" << endl;
+volScalarField T
+(
+    IOobject
+    (
+        "T",
+        runTime.timeName(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::AUTO_WRITE
+    ),
+    mesh
+);
+
+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"
+
+#include "readTransportProperties.H"
+
+Info<< "Creating turbulence model\n" << endl;
+autoPtr<incompressible::turbulenceModel> turbulence
+(
+    incompressible::turbulenceModel::New(U, phi, laminarTransport)
+);
+
+// Kinematic density for buoyancy force
+volScalarField rhok
+(
+    IOobject
+    (
+        "rhok",
+        runTime.timeName(),
+        mesh
+    ),
+    1.0 - beta*(T - TRef)
+);
+
+// kinematic turbulent thermal thermal conductivity m2/s
+Info<< "Reading field alphat\n" << endl;
+volScalarField alphat
+(
+    IOobject
+    (
+        "alphat",
+        runTime.timeName(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::AUTO_WRITE
+    ),
+    mesh
+);
+
+
+#include "readGravitationalAcceleration.H"
+#include "readhRef.H"
+#include "gh.H"
+
+
+volScalarField p
+(
+    IOobject
+    (
+        "p",
+        runTime.timeName(),
+        mesh,
+        IOobject::NO_READ,
+        IOobject::AUTO_WRITE
+    ),
+    p_rgh + rhok*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)
+    );
+}
+
+mesh.setFluxRequired(p_rgh.name());
+
+#include "createMRF.H"
+#include "createIncompressibleRadiationModel.H"
+#include "createFvOptions.H"

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqPimpleFoam/pEqn.H

+{
+    volScalarField rAU("rAU", 1.0/UEqn.A());
+    surfaceScalarField rAUf("rAUf", fvc::interpolate(rAU));
+    volVectorField HbyA(constrainHbyA(rAU*UEqn.H(), U, p_rgh));
+
+    surfaceScalarField phig(-rAUf*ghf*fvc::snGrad(rhok)*mesh.magSf());
+
+    surfaceScalarField phiHbyA
+    (
+        "phiHbyA",
+        fvc::flux(HbyA)
+      + MRF.zeroFilter(rAUf*fvc::ddtCorr(U, phi))
+      + phig
+    );
+
+    MRF.makeRelative(phiHbyA);
+
+    // 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())
+        {
+            // Calculate the conservative fluxes
+            phi = phiHbyA - p_rghEqn.flux();
+
+            // Explicitly relax pressure for momentum corrector
+            p_rgh.relax();
+
+            // Correct the momentum source with the pressure gradient flux
+            // calculated from the relaxed pressure
+            U = HbyA + rAU*fvc::reconstruct((phig - p_rghEqn.flux())/rAUf);
+            U.correctBoundaryConditions();
+            fvOptions.correct(U);
+
+            // Correct Uf if the mesh is moving
+            fvc::correctUf(Uf, U, phi);
+
+            // Make the fluxes relative to the mesh motion
+            fvc::makeRelative(phi, U);
+        }
+    }
+
+    #include "continuityErrs.H"
+
+    p = p_rgh + rhok*gh;
+
+    if (p_rgh.needReference())
+    {
+        p += dimensionedScalar
+        (
+            "p",
+            p.dimensions(),
+            pRefValue - getRefCellValue(p, pRefCell)
+        );
+        p_rgh = p - rhok*gh;
+    }
+}

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqSimpleFoam/Make/files

+buoyantBoussinesqSimpleFoam.C
+
+EXE = $(FOAM_APPBIN)/buoyantBoussinesqSimpleFoam

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqSimpleFoam/Make/options

+EXE_INC = \
+    -I$(LIB_SRC)/finiteVolume/lnInclude \
+    -I$(LIB_SRC)/meshTools/lnInclude \
+    -I$(LIB_SRC)/sampling/lnInclude \
+    -I$(LIB_SRC)/TurbulenceModels/turbulenceModels/lnInclude \
+    -I$(LIB_SRC)/TurbulenceModels/incompressible/lnInclude \
+    -I$(LIB_SRC)/transportModels \
+    -I$(LIB_SRC)/transportModels/incompressible/singlePhaseTransportModel \
+    -I$(LIB_SRC)/thermophysicalModels/radiation/lnInclude
+
+EXE_LIBS = \
+    -lfiniteVolume \
+    -lfvOptions \
+    -lmeshTools \
+    -lsampling \
+    -lturbulenceModels \
+    -lincompressibleTurbulenceModels \
+    -lincompressibleTransportModels \
+    -lradiationModels \
+    -latmosphericModels

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqSimpleFoam/TEqn.H

+{
+    alphat = turbulence->nut()/Prt;
+    alphat.correctBoundaryConditions();
+
+    volScalarField alphaEff("alphaEff", turbulence->nu()/Pr + alphat);
+
+    fvScalarMatrix TEqn
+    (
+        fvm::div(phi, T)
+      - fvm::laplacian(alphaEff, T)
+     ==
+        radiation->ST(rhoCpRef, T)
+      + fvOptions(T)
+    );
+
+    TEqn.relax();
+
+    fvOptions.constrain(TEqn);
+
+    TEqn.solve();
+
+    radiation->correct();
+
+    fvOptions.correct(T);
+
+    rhok = 1.0 - beta*(T - TRef);
+}

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqSimpleFoam/UEqn.H

+    // Solve the momentum equation
+
+    MRF.correctBoundaryVelocity(U);
+
+    tmp<fvVectorMatrix> tUEqn
+    (
+        fvm::div(phi, U)
+      + MRF.DDt(U)
+      + turbulence->divDevReff(U)
+     ==
+        fvOptions(U)
+    );
+    fvVectorMatrix& UEqn = tUEqn.ref();
+
+    UEqn.relax();
+
+    fvOptions.constrain(UEqn);
+
+    if (simple.momentumPredictor())
+    {
+        solve
+        (
+            UEqn
+          ==
+            fvc::reconstruct
+            (
+                (
+                  - ghf*fvc::snGrad(rhok)
+                  - fvc::snGrad(p_rgh)
+                )*mesh.magSf()
+            )
+        );
+
+        fvOptions.correct(U);
+    }

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqSimpleFoam/buoyantBoussinesqSimpleFoam.C

+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2011-2017 OpenFOAM Foundation
+-------------------------------------------------------------------------------
+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
+    buoyantBoussinesqSimpleFoam
+
+Group
+    grpHeatTransferSolvers
+
+Description
+    Steady-state solver for buoyant, turbulent flow of incompressible fluids.
+
+    Uses the Boussinesq approximation:
+    \f[
+        rho_{k} = 1 - beta(T - T_{ref})
+    \f]
+
+    where:
+        \f$ rho_{k} \f$ = the effective (driving) density
+        beta = thermal expansion coefficient [1/K]
+        T = temperature [K]
+        \f$ T_{ref} \f$ = reference temperature [K]
+
+    Valid when:
+    \f[
+        \frac{beta(T - T_{ref})}{rho_{ref}} << 1
+    \f]
+
+\*---------------------------------------------------------------------------*/
+
+#include "fvCFD.H"
+#include "singlePhaseTransportModel.H"
+#include "turbulentTransportModel.H"
+#include "radiationModel.H"
+#include "fvOptions.H"
+#include "simpleControl.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+int main(int argc, char *argv[])
+{
+    argList::addNote
+    (
+        "Steady-state solver for buoyant, turbulent flow"
+        " of incompressible fluids."
+    );
+
+    #include "postProcess.H"
+
+    #include "addCheckCaseOptions.H"
+    #include "setRootCaseLists.H"
+    #include "createTime.H"
+    #include "createMesh.H"
+    #include "createControl.H"
+    #include "createFields.H"
+    #include "initContinuityErrs.H"
+
+    turbulence->validate();
+
+    // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+    Info<< "\nStarting time loop\n" << endl;
+
+    while (simple.loop())
+    {
+        Info<< "Time = " << runTime.timeName() << nl << endl;
+
+        // Pressure-velocity SIMPLE corrector
+        {
+            #include "UEqn.H"
+            #include "TEqn.H"
+            #include "pEqn.H"
+        }
+
+        laminarTransport.correct();
+        turbulence->correct();
+
+        runTime.write();
+
+        runTime.printExecutionTime(Info);
+    }
+
+    Info<< "End\n" << endl;
+
+    return 0;
+}
+
+
+// ************************************************************************* //

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqSimpleFoam/createFields.H

+Info<< "Reading thermophysical properties\n" << endl;
+
+Info<< "Reading field T\n" << endl;
+volScalarField T
+(
+    IOobject
+    (
+        "T",
+        runTime.timeName(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::AUTO_WRITE
+    ),
+    mesh
+);
+
+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"
+
+#include "readTransportProperties.H"
+
+Info<< "Creating turbulence model\n" << endl;
+autoPtr<incompressible::turbulenceModel> turbulence
+(
+    incompressible::turbulenceModel::New(U, phi, laminarTransport)
+);
+
+// Kinematic density for buoyancy force
+volScalarField rhok
+(
+    IOobject
+    (
+        "rhok",
+        runTime.timeName(),
+        mesh
+    ),
+    1.0 - beta*(T - TRef)
+);
+
+// kinematic turbulent thermal thermal conductivity m2/s
+Info<< "Reading field alphat\n" << endl;
+volScalarField alphat
+(
+    IOobject
+    (
+        "alphat",
+        runTime.timeName(),
+        mesh,
+        IOobject::MUST_READ,
+        IOobject::AUTO_WRITE
+    ),
+    mesh
+);
+
+
+#include "readGravitationalAcceleration.H"
+#include "readhRef.H"
+#include "gh.H"
+
+
+volScalarField p
+(
+    IOobject
+    (
+        "p",
+        runTime.timeName(),
+        mesh,
+        IOobject::NO_READ,
+        IOobject::AUTO_WRITE
+    ),
+    p_rgh + rhok*gh
+);
+
+label pRefCell = 0;
+scalar pRefValue = 0.0;
+setRefCell
+(
+    p,
+    p_rgh,
+    simple.dict(),
+    pRefCell,
+    pRefValue
+);
+
+if (p_rgh.needReference())
+{
+    p += dimensionedScalar
+    (
+        "p",
+        p.dimensions(),
+        pRefValue - getRefCellValue(p, pRefCell)
+    );
+}
+
+mesh.setFluxRequired(p_rgh.name());
+
+#include "createMRF.H"
+#include "createIncompressibleRadiationModel.H"
+#include "createFvOptions.H"

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqSimpleFoam/pEqn.H

+{
+    volScalarField rAU("rAU", 1.0/UEqn.A());
+    surfaceScalarField rAUf("rAUf", fvc::interpolate(rAU));
+    volVectorField HbyA(constrainHbyA(rAU*UEqn.H(), U, p_rgh));
+
+    tUEqn.clear();
+
+    surfaceScalarField phig(-rAUf*ghf*fvc::snGrad(rhok)*mesh.magSf());
+
+    surfaceScalarField phiHbyA
+    (
+        "phiHbyA",
+        fvc::flux(HbyA)
+    );
+
+    MRF.makeRelative(phiHbyA);
+
+    adjustPhi(phiHbyA, U, p_rgh);
+
+    phiHbyA += phig;
+
+    // Update the pressure BCs to ensure flux consistency
+    constrainPressure(p_rgh, U, phiHbyA, rAUf, MRF);
+
+    while (simple.correctNonOrthogonal())
+    {
+        fvScalarMatrix p_rghEqn
+        (
+            fvm::laplacian(rAUf, p_rgh) == fvc::div(phiHbyA)
+        );
+
+        p_rghEqn.setReference(pRefCell, getRefCellValue(p_rgh, pRefCell));
+
+        p_rghEqn.solve();
+
+        if (simple.finalNonOrthogonalIter())
+        {
+            // Calculate the conservative fluxes
+            phi = phiHbyA - p_rghEqn.flux();
+
+            // Explicitly relax pressure for momentum corrector
+            p_rgh.relax();
+
+            // Correct the momentum source with the pressure gradient flux
+            // calculated from the relaxed pressure
+            U = HbyA + rAU*fvc::reconstruct((phig - p_rghEqn.flux())/rAUf);
+            U.correctBoundaryConditions();
+            fvOptions.correct(U);
+        }
+    }
+
+    #include "continuityErrs.H"
+
+    p = p_rgh + rhok*gh;
+
+    if (p_rgh.needReference())
+    {
+        p += dimensionedScalar
+        (
+            "p",
+            p.dimensions(),
+            pRefValue - getRefCellValue(p, pRefCell)
+        );
+        p_rgh = p - rhok*gh;
+    }
+}

OpenFOAM-v2112/applications/solvers/heatTransfer/buoyantBoussinesqSimpleFoam/readTransportProperties.H

+singlePhaseTransportModel laminarTransport(U, phi);
+
+// Thermal expansion coefficient [1/K]
+dimensionedScalar beta
+(
+    "beta",
+    dimless/dimTemperature,
+    laminarTransport
+);
+
+// Reference temperature [K]
+dimensionedScalar TRef("TRef", dimTemperature, laminarTransport);
+
+// Laminar Prandtl number
+dimensionedScalar Pr("Pr", dimless, laminarTransport);
+
+// Turbulent Prandtl number
+dimensionedScalar Prt("Prt", dimless, laminarTransport);