fourthGrad.C

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#include "fourthGrad.H"
#include <finiteVolume/leastSquaresGrad.H>
#include <finiteVolume/gaussGrad.H>
#include <finiteVolume/fvMesh.H>
#include <finiteVolume/volMesh.H>
#include <finiteVolume/surfaceMesh.H>
#include <OpenFOAM/GeometricField.H>
#include <finiteVolume/zeroGradientFvPatchField.H>

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

namespace Foam
{

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

namespace fv
{

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

template<class Type>
tmp
<
    GeometricField
    <
        typename outerProduct<vector, Type>::type, fvPatchField, volMesh
    >
>
fourthGrad<Type>::grad
(
    const GeometricField<Type, fvPatchField, volMesh>& vsf
) const
{
    // The fourth-order gradient is calculated in two passes.  First,
    // the standard least-square gradient is assembled.  Then, the
    // fourth-order correction is added to the second-order accurate
    // gradient to complete the accuracy.

    typedef typename outerProduct<vector, Type>::type GradType;

    const fvMesh& mesh = vsf.mesh();

    // Assemble the second-order least-square gradient
    // Calculate the second-order least-square gradient
    tmp<GeometricField<GradType, fvPatchField, volMesh> > tsecondfGrad
        = leastSquaresGrad<Type>(mesh).grad(vsf);
    const GeometricField<GradType, fvPatchField, volMesh>& secondfGrad =
        tsecondfGrad();

    tmp<GeometricField<GradType, fvPatchField, volMesh> > tfGrad
    (
        new GeometricField<GradType, fvPatchField, volMesh>
        (
            IOobject
            (
                "grad("+vsf.name()+')',
                vsf.instance(),
                mesh,
                IOobject::NO_READ,
                IOobject::NO_WRITE
            ),
            secondfGrad
        )
    );
    GeometricField<GradType, fvPatchField, volMesh>& fGrad = tfGrad();

    const vectorField& C = mesh.C();

    const surfaceScalarField& lambda = mesh.weights();

    // Get reference to least square vectors
    const leastSquaresVectors& lsv = leastSquaresVectors::New(mesh);
    const surfaceVectorField& ownLs = lsv.pVectors();
    const surfaceVectorField& neiLs = lsv.nVectors();

    // owner/neighbour addressing
    const unallocLabelList& own = mesh.owner();
    const unallocLabelList& nei = mesh.neighbour();

    // Assemble the fourth-order gradient

    // Internal faces
    forAll(own, facei)
    {
        Type dDotGradDelta = 0.5*
        (
           (C[nei[facei]] - C[own[facei]])
         & (secondfGrad[nei[facei]] - secondfGrad[own[facei]])
        );

        fGrad[own[facei]] -= lambda[facei]*ownLs[facei]*dDotGradDelta;
        fGrad[nei[facei]] -= (1.0 - lambda[facei])*neiLs[facei]*dDotGradDelta;
    }

    // Boundary faces
    forAll(vsf.boundaryField(), patchi)
    {
        if (secondfGrad.boundaryField()[patchi].coupled())
        {
            const fvsPatchVectorField& patchOwnLs =
                ownLs.boundaryField()[patchi];

            const scalarField& lambdap = lambda.boundaryField()[patchi];

            // Build the d-vectors
            vectorField pd = 
                mesh.Sf().boundaryField()[patchi]
               /(
                   mesh.magSf().boundaryField()[patchi]
                  *mesh.deltaCoeffs().boundaryField()[patchi]
                );

            if (!mesh.orthogonal())
            {
                pd -= mesh.correctionVectors().boundaryField()[patchi]
                     /mesh.deltaCoeffs().boundaryField()[patchi];
            }

            const unallocLabelList& faceCells =
                fGrad.boundaryField()[patchi].patch().faceCells();

            Field<GradType> neighbourSecondfGrad =
                secondfGrad.boundaryField()[patchi].patchNeighbourField();

            forAll(faceCells, patchFaceI)
            {
                fGrad[faceCells[patchFaceI]] -=
                    0.5*lambdap[patchFaceI]*patchOwnLs[patchFaceI]
                   *(
                        pd[patchFaceI]
                      & (
                            neighbourSecondfGrad[patchFaceI]
                          - secondfGrad[faceCells[patchFaceI]]
                        )
                    );
            }
        }
    }

    fGrad.correctBoundaryConditions();
    gaussGrad<Type>::correctBoundaryConditions(vsf, fGrad);

    return tfGrad;
}


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

} // End namespace fv

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

} // End namespace Foam

// ************************ vim: set sw=4 sts=4 et: ************************ //