[ztdep]

I Cann't find the step to solve the least square problem Ax=b for the gradient. Could you give me some suggestions

template<class Type>
Foam::tmp
<
    Foam::GeometricField
    <
        typename Foam::outerProduct<Foam::vector, Type>::type,
        Foam::fvPatchField,
        Foam::volMesh
    >
>
Foam::fv::leastSquaresGrad<Type>::calcGrad
(
    const GeometricField<Type, fvPatchField, volMesh>& vsf,
    const word& name
) const
{
    typedef typename outerProduct<vector, Type>::type GradType;

    const fvMesh& mesh = vsf.mesh();

    tmp<GeometricField<GradType, fvPatchField, volMesh>> tlsGrad
    (
        new GeometricField<GradType, fvPatchField, volMesh>
        (
            IOobject
            (
                name,
                vsf.instance(),
                mesh,
                IOobject::NO_READ,
                IOobject::NO_WRITE
            ),
            mesh,
            dimensioned<GradType>(vsf.dimensions()/dimLength, Zero),
            extrapolatedCalculatedFvPatchField<GradType>::typeName
        )
    );
    GeometricField<GradType, fvPatchField, volMesh>& lsGrad = tlsGrad.ref();

    // Get reference to least square vectors
    const leastSquaresVectors& lsv = leastSquaresVectors::New(mesh);

    const surfaceVectorField& ownLs = lsv.pVectors();
    const surfaceVectorField& neiLs = lsv.nVectors();

    const labelUList& own = mesh.owner();
    const labelUList& nei = mesh.neighbour();

    forAll(own, facei)
    {
        label ownFacei = own[facei];
        label neiFacei = nei[facei];

        Type deltaVsf = vsf[neiFacei] - vsf[ownFacei];

        lsGrad[ownFacei] += ownLs[facei]*deltaVsf;
        lsGrad[neiFacei] -= neiLs[facei]*deltaVsf;
    }

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

        const labelUList& faceCells =
            vsf.boundaryField()[patchi].patch().faceCells();

        if (vsf.boundaryField()[patchi].coupled())
        {
            const Field<Type> neiVsf
            (
                vsf.boundaryField()[patchi].patchNeighbourField()
            );

            forAll(neiVsf, patchFacei)
            {
                lsGrad[faceCells[patchFacei]] +=
                    patchOwnLs[patchFacei]
                   *(neiVsf[patchFacei] - vsf[faceCells[patchFacei]]);
            }
        }
        else
        {
            const fvPatchField<Type>& patchVsf = vsf.boundaryField()[patchi];

            forAll(patchVsf, patchFacei)
            {
                lsGrad[faceCells[patchFacei]] +=
                     patchOwnLs[patchFacei]
                    *(patchVsf[patchFacei] - vsf[faceCells[patchFacei]]);
            }
        }
    }


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

    return tlsGrad;
}

[clapointe]

Is it not in leastSquaresVectors? A quick look at that code reveals that it contains an inversion step. Note I've not done a deep dive into the code, but it looks like a good place to start.

Caelan

[ztdep]

Originally Posted by clapointe

Is it not in leastSquaresVectors? A quick look at that code reveals that it contains an inversion step. Note I've not done a deep dive into the code, but it looks like a good place to start.

Caelan

Thanks a lot, i have find it. It was calculated in the constructor().

[santiagomarquezd]

Hi, its is done in two steps, the geometrical part (this not change if mesh is static) is precomputed in leastSquaresVectors, then the gradient is finally computed in calcGrad method.

Regards!