ENH: gradSchemes: new gradient scheme iterativeGaussGrad

A second-order gradient scheme using face-interpolation,
Gauss' theorem and iterative skew correction.

Minimal example by using system/fvSchemes:

  gradSchemes
  {
    grad(<term>) iterativeGauss <interpolation scheme> <number of iters>;
  }

src/finiteVolume/Make/files

@@ -433,6 +433,7 @@ $(divSchemes)/gaussDivScheme/gaussDivSchemes.C
 gradSchemes = finiteVolume/gradSchemes
 $(gradSchemes)/gradScheme/gradSchemes.C
 $(gradSchemes)/gaussGrad/gaussGrads.C
+$(gradSchemes)/iterativeGaussGrad/iterativeGaussGrads.C
 
 $(gradSchemes)/leastSquaresGrad/leastSquaresVectors.C
 $(gradSchemes)/leastSquaresGrad/leastSquaresGrads.C

src/finiteVolume/finiteVolume/gradSchemes/iterativeGaussGrad/iterativeGaussGrad.C

@@ -0,0 +1,92 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    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/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "iterativeGaussGrad.H"
+#include "skewCorrectionVectors.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+template<class Type>
+Foam::tmp
+<
+    Foam::GeometricField
+    <
+        typename Foam::outerProduct<Foam::vector, Type>::type,
+        Foam::fvPatchField,
+        Foam::volMesh
+    >
+>
+Foam::fv::iterativeGaussGrad<Type>::calcGrad
+(
+    const GeometricField<Type, fvPatchField, volMesh>& vsf,
+    const word& name
+) const
+{
+    typedef typename outerProduct<vector, Type>::type GradType;
+    typedef GeometricField<GradType, fvPatchField, volMesh> GradFieldType;
+    typedef GeometricField<GradType, fvsPatchField, surfaceMesh>
+        GradSurfFieldType;
+    typedef GeometricField<Type, fvsPatchField, surfaceMesh> SurfFieldType;
+
+    tmp<SurfFieldType> tssf = linearInterpolate(vsf);
+    const SurfFieldType& ssf = tssf.cref();
+
+    tmp<GradFieldType> tgGrad = fv::gaussGrad<Type>::gradf(ssf, name);
+    GradFieldType& gGrad = tgGrad.ref();
+
+    const skewCorrectionVectors& skv = skewCorrectionVectors::New(vsf.mesh());
+
+    for (label i = 0; i < nIter_; ++i)
+    {
+        tmp<GradSurfFieldType> tsgGrad = linearInterpolate(gGrad);
+
+        tmp<SurfFieldType> tcorr = skv() & tsgGrad;
+
+        tcorr.ref().dimensions().reset(vsf.dimensions());
+
+        if (vsf.mesh().relaxField("grad(" + vsf.name() + ")"))
+        {
+            const scalar relax =
+                vsf.mesh().fieldRelaxationFactor("grad(" + vsf.name() + ")");
+
+            // relax*prediction + (1-relax)*old
+            gGrad *= (1.0 - relax);
+            gGrad += relax*fv::gaussGrad<Type>::gradf(tcorr + ssf, name);
+        }
+        else
+        {
+            gGrad = fv::gaussGrad<Type>::gradf(tcorr + ssf, name);
+        }
+    }
+
+    fv::gaussGrad<Type>::correctBoundaryConditions(vsf, gGrad);
+
+    return tgGrad;
+}
+
+
+// ************************************************************************* //

src/finiteVolume/finiteVolume/gradSchemes/iterativeGaussGrad/iterativeGaussGrad.H

@@ -0,0 +1,166 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    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/>.
+
+Class
+    Foam::fv::iterativeGaussGrad
+
+Description
+    A second-order gradient scheme using face-interpolation,
+    Gauss' theorem and iterative skew correction.
+
+Usage
+    Minimal example by using \c system/fvSchemes:
+    \verbatim
+    gradSchemes
+    {
+        grad(<term>)   iterativeGauss <interpolation scheme> <number of iters>;
+    }
+    \endverbatim
+
+    and by using \c system/fvSolution:
+    \verbatim
+    relaxationFactors
+    {
+        fields
+        {
+            grad(<term>)    <relaxation factor>;
+        }
+    }
+    \endverbatim
+
+SourceFiles
+    iterativeGaussGrad.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef iterativeGaussGrad_H
+#define iterativeGaussGrad_H
+
+#include "gaussGrad.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace fv
+{
+
+/*---------------------------------------------------------------------------*\
+                       Class iterativeGaussGrad Declaration
+\*---------------------------------------------------------------------------*/
+
+template<class Type>
+class iterativeGaussGrad
+:
+    public fv::gaussGrad<Type>
+{
+    // Private Data
+
+        //- Number of skew-correction iterations
+        label nIter_;
+
+
+    // Private Member Functions
+
+        //- No copy construct
+        iterativeGaussGrad(const iterativeGaussGrad&) = delete;
+
+        //- No copy assignment
+        void operator=(const iterativeGaussGrad&) = delete;
+
+
+public:
+
+    //- Runtime type information
+    TypeName("iterativeGauss");
+
+
+    // Constructors
+
+        //- Construct from mesh
+        iterativeGaussGrad(const fvMesh& mesh)
+        :
+            gaussGrad<Type>(mesh),
+            nIter_(1)
+        {}
+
+        //- Construct from mesh and Istream
+        iterativeGaussGrad(const fvMesh& mesh, Istream& schemeData)
+        :
+            gaussGrad<Type>(mesh, schemeData),
+            nIter_(readLabel(schemeData))
+        {
+            if (nIter_ <= 0)
+            {
+                FatalIOErrorInFunction(schemeData)
+                    << "nIter = " << nIter_
+                    << " should be > 0"
+                    << exit(FatalIOError);
+            }
+        }
+
+
+    // Member Functions
+
+        //- Return the gradient of the given field
+        //- to the gradScheme::grad for optional caching
+        virtual tmp
+        <
+            GeometricField
+            <
+                typename outerProduct<vector, Type>::type,
+                fvPatchField,
+                volMesh
+            >
+        > calcGrad
+        (
+            const GeometricField<Type, fvPatchField, volMesh>& vsf,
+            const word& name
+        ) const;
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace fv
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#ifdef NoRepository
+    #include "iterativeGaussGrad.C"
+#endif
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //

src/finiteVolume/finiteVolume/gradSchemes/iterativeGaussGrad/iterativeGaussGrads.C

@@ -0,0 +1,34 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    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/>.
+
+\*---------------------------------------------------------------------------*/
+
+#include "iterativeGaussGrad.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+makeFvGradScheme(iterativeGaussGrad)
+
+// ************************************************************************* //