EulerD2dt2Scheme.C

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#include "EulerD2dt2Scheme.H"
#include "fvcDiv.H"
#include "fvMatrices.H"

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

namespace Foam
{

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

namespace fv
{

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

template<class Type>
tmp<GeometricField<Type, fvPatchField, volMesh>>
EulerD2dt2Scheme<Type>::fvcD2dt2
(
    const GeometricField<Type, fvPatchField, volMesh>& vf
)
{
    const dimensionedScalar rDeltaT2
    (
        4.0/sqr(mesh().time().deltaT() + mesh().time().deltaT0())
    );

    const word d2dt2name("d2dt2("+vf.name()+')');

    const scalar deltaT = mesh().time().deltaTValue();
    const scalar deltaT0 = mesh().time().deltaT0Value();

    const scalar coefft   = (deltaT + deltaT0)/(2*deltaT);
    const scalar coefft00 = (deltaT + deltaT0)/(2*deltaT0);
    const scalar coefft0  = coefft + coefft00;

    if (mesh().moving())
    {
        const dimensionedScalar halfRdeltaT2(rDeltaT2/2.0);

        const volScalarField::Internal VV0(mesh().V() + mesh().V0());
        const volScalarField::Internal V0V00(mesh().V0() + mesh().V00());

        return GeometricField<Type, fvPatchField, volMesh>::New
        (
            d2dt2name,
            halfRdeltaT2*
            (
                coefft*VV0*vf()

              - (coefft*VV0 + coefft00*V0V00)
               *vf.oldTime()()

              + (coefft00*V0V00)*vf.oldTime().oldTime()()
            )/mesh().V(),
            rDeltaT2.value()*
            (
                coefft*vf.boundaryField()
              - coefft0*vf.oldTime().boundaryField()
              + coefft00*vf.oldTime().oldTime().boundaryField()
            )
        );
    }
    else
    {
        return GeometricField<Type, fvPatchField, volMesh>::New
        (
            d2dt2name,
            rDeltaT2*
            (
                coefft*vf
              - coefft0*vf.oldTime()
              + coefft00*vf.oldTime().oldTime()
            )
        );
    }
}


template<class Type>
tmp<GeometricField<Type, fvPatchField, volMesh>>
EulerD2dt2Scheme<Type>::fvcD2dt2
(
    const volScalarField& rho,
    const GeometricField<Type, fvPatchField, volMesh>& vf
)
{
    const dimensionedScalar rDeltaT2
    (
        4.0/sqr(mesh().time().deltaT() + mesh().time().deltaT0())
    );

    const word d2dt2name("d2dt2("+rho.name()+','+vf.name()+')');

    const scalar deltaT = mesh().time().deltaTValue();
    const scalar deltaT0 = mesh().time().deltaT0Value();

    const scalar coefft   = (deltaT + deltaT0)/(2*deltaT);
    const scalar coefft00 = (deltaT + deltaT0)/(2*deltaT0);

    if (mesh().moving())
    {
        const dimensionedScalar halfRdeltaT2(0.5*rDeltaT2);
        const dimensionedScalar quarterRdeltaT2(0.25*rDeltaT2);

        const volScalarField::Internal VV0rhoRho0
        (
            (mesh().V() + mesh().V0())*(rho() + rho.oldTime()())
        );

        const volScalarField::Internal V0V00rho0Rho00
        (
            (mesh().V0() + mesh().V00())
           *(
                rho.oldTime()()
              + rho.oldTime().oldTime()()
            )
        );

        return GeometricField<Type, fvPatchField, volMesh>::New
        (
            d2dt2name,
            quarterRdeltaT2*
            (
                coefft*VV0rhoRho0*vf()

              - (coefft*VV0rhoRho0 + coefft00*V0V00rho0Rho00)
               *vf.oldTime()()

              + (coefft00*V0V00rho0Rho00)
               *vf.oldTime().oldTime()()
            )/mesh().V(),
            halfRdeltaT2.value()*
            (
                coefft
               *(rho.boundaryField() + rho.oldTime().boundaryField())
               *vf.boundaryField()

              - (
                    coefft
                   *(
                       rho.boundaryField()
                     + rho.oldTime().boundaryField()
                    )
                  + coefft00
                   *(
                       rho.oldTime().boundaryField()
                     + rho.oldTime().oldTime().boundaryField()
                    )
                )*vf.oldTime().boundaryField()

              + coefft00
               *(
                   rho.oldTime().boundaryField()
                 + rho.oldTime().oldTime().boundaryField()
                )*vf.oldTime().oldTime().boundaryField()
            )
        );
    }
    else
    {
        const dimensionedScalar halfRdeltaT2 = 0.5*rDeltaT2;

        const volScalarField rhoRho0(rho + rho.oldTime());
        const volScalarField rho0Rho00(rho.oldTime() +rho.oldTime().oldTime());

        return GeometricField<Type, fvPatchField, volMesh>::New
        (
            d2dt2name,
            halfRdeltaT2*
            (
                coefft*rhoRho0*vf
              - (coefft*rhoRho0 + coefft00*rho0Rho00)*vf.oldTime()
              + coefft00*rho0Rho00*vf.oldTime().oldTime()
            )
        );
    }
}


template<class Type>
tmp<fvMatrix<Type>>
EulerD2dt2Scheme<Type>::fvmD2dt2
(
    const GeometricField<Type, fvPatchField, volMesh>& vf
)
{
    tmp<fvMatrix<Type>> tfvm
    (
        new fvMatrix<Type>
        (
            vf,
            vf.dimensions()*dimVol/dimTime/dimTime
        )
    );

    fvMatrix<Type>& fvm = tfvm.ref();

    const scalar deltaT = mesh().time().deltaTValue();
    const scalar deltaT0 = mesh().time().deltaT0Value();

    const scalar coefft   = (deltaT + deltaT0)/(2*deltaT);
    const scalar coefft00 = (deltaT + deltaT0)/(2*deltaT0);
    const scalar coefft0  = coefft + coefft00;

    const scalar rDeltaT2 = 4.0/sqr(deltaT + deltaT0);

    if (mesh().moving())
    {
        const scalar halfRdeltaT2 = rDeltaT2/2.0;

        const scalarField VV0(mesh().V() + mesh().V0());
        const scalarField V0V00(mesh().V0() + mesh().V00());

        fvm.diag() = (coefft*halfRdeltaT2)*VV0;

        fvm.source() = halfRdeltaT2*
        (
            (coefft*VV0 + coefft00*V0V00)
           *vf.oldTime().primitiveField()

          - (coefft00*V0V00)*vf.oldTime().oldTime().primitiveField()
        );
    }
    else
    {
        fvm.diag() = (coefft*rDeltaT2)*mesh().V();

        fvm.source() = rDeltaT2*mesh().V()*
        (
            coefft0*vf.oldTime().primitiveField()
          - coefft00*vf.oldTime().oldTime().primitiveField()
        );
    }

    return tfvm;
}


template<class Type>
tmp<fvMatrix<Type>>
EulerD2dt2Scheme<Type>::fvmD2dt2
(
    const dimensionedScalar& rho,
    const GeometricField<Type, fvPatchField, volMesh>& vf
)
{
    tmp<fvMatrix<Type>> tfvm
    (
        new fvMatrix<Type>
        (
            vf,
            rho.dimensions()*vf.dimensions()*dimVol
            /dimTime/dimTime
        )
    );

    fvMatrix<Type>& fvm = tfvm.ref();

    const scalar deltaT = mesh().time().deltaTValue();
    const scalar deltaT0 = mesh().time().deltaT0Value();

    const scalar coefft   = (deltaT + deltaT0)/(2*deltaT);
    const scalar coefft00 = (deltaT + deltaT0)/(2*deltaT0);

    const scalar rDeltaT2 = 4.0/sqr(deltaT + deltaT0);

    if (mesh().moving())
    {
        const scalar halfRdeltaT2 = 0.5*rDeltaT2;

        const scalarField VV0(mesh().V() + mesh().V0());
        const scalarField V0V00(mesh().V0() + mesh().V00());

        fvm.diag() = rho.value()*(coefft*halfRdeltaT2)*VV0;

        fvm.source() = halfRdeltaT2*rho.value()*
        (
            (coefft*VV0 + coefft00*V0V00)
           *vf.oldTime().primitiveField()

          - (coefft00*V0V00)*vf.oldTime().oldTime().primitiveField()
        );
    }
    else
    {
        fvm.diag() = (coefft*rDeltaT2)*mesh().V()*rho.value();

        fvm.source() = rDeltaT2*mesh().V()*rho.value()*
        (
            (coefft + coefft00)*vf.oldTime().primitiveField()
          - coefft00*vf.oldTime().oldTime().primitiveField()
        );
    }

    return tfvm;
}


template<class Type>
tmp<fvMatrix<Type>>
EulerD2dt2Scheme<Type>::fvmD2dt2
(
    const volScalarField& rho,
    const GeometricField<Type, fvPatchField, volMesh>& vf
)
{
    tmp<fvMatrix<Type>> tfvm
    (
        new fvMatrix<Type>
        (
            vf,
            rho.dimensions()*vf.dimensions()*dimVol
            /dimTime/dimTime
        )
    );

    fvMatrix<Type>& fvm = tfvm.ref();

    const scalar deltaT = mesh().time().deltaTValue();
    const scalar deltaT0 = mesh().time().deltaT0Value();

    const scalar coefft   = (deltaT + deltaT0)/(2*deltaT);
    const scalar coefft00 = (deltaT + deltaT0)/(2*deltaT0);

    const scalar rDeltaT2 = 4.0/sqr(deltaT + deltaT0);

    if (mesh().moving())
    {
        const scalar quarterRdeltaT2 = 0.25*rDeltaT2;

        const scalarField VV0rhoRho0
        (
            (mesh().V() + mesh().V0())
           *(rho.primitiveField() + rho.oldTime().primitiveField())
        );

        const scalarField V0V00rho0Rho00
        (
            (mesh().V0() + mesh().V00())
           *(
               rho.oldTime().primitiveField()
             + rho.oldTime().oldTime().primitiveField()
            )
        );

        fvm.diag() = (coefft*quarterRdeltaT2)*VV0rhoRho0;

        fvm.source() = quarterRdeltaT2*
        (
            (coefft*VV0rhoRho0 + coefft00*V0V00rho0Rho00)
           *vf.oldTime().primitiveField()

          - (coefft00*V0V00rho0Rho00)
           *vf.oldTime().oldTime().primitiveField()
        );
    }
    else
    {
        const scalar halfRdeltaT2 = 0.5*rDeltaT2;

        const scalarField rhoRho0
        (
            rho.primitiveField()
          + rho.oldTime().primitiveField()
        );

        const scalarField rho0Rho00
        (
            rho.oldTime().primitiveField()
          + rho.oldTime().oldTime().primitiveField()
        );

        fvm.diag() = (coefft*halfRdeltaT2)*mesh().V()*rhoRho0;

        fvm.source() = halfRdeltaT2*mesh().V()*
        (
            (coefft*rhoRho0 + coefft00*rho0Rho00)
           *vf.oldTime().primitiveField()

          - (coefft00*rho0Rho00)
           *vf.oldTime().oldTime().primitiveField()
        );
    }

    return tfvm;
}


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

} // End namespace fv

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

} // End namespace Foam

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