cctpfa/forchheimerslaw.hh

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#ifndef DUMUX_DISCRETIZATION_CC_TPFA_FORCHHEIMERS_LAW_HH
#define DUMUX_DISCRETIZATION_CC_TPFA_FORCHHEIMERS_LAW_HH
 
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
 
#include <dumux/common/math.hh>
#include <dumux/common/parameters.hh>
#include <dumux/common/properties.hh>
#include <dumux/common/typetraits/typetraits.hh>
 
#include <dumux/discretization/method.hh>
#include <dumux/discretization/extrusion.hh>
#include <dumux/flux/cctpfa/darcyslaw.hh>
 
namespace Dumux {
 
// forward declarations
template<class TypeTag, class ForchheimerVelocity, class DiscretizationMethod>
class ForchheimersLawImplementation;

template<class Scalar, class GridGeometry, class ForchheimerVelocity, bool isNetwork>
class CCTpfaForchheimersLaw;

template <class TypeTag, class ForchheimerVelocity>
class ForchheimersLawImplementation<TypeTag, ForchheimerVelocity, DiscretizationMethods::CCTpfa>
: public CCTpfaForchheimersLaw<GetPropType<TypeTag, Properties::Scalar>,
                               GetPropType<TypeTag, Properties::GridGeometry>,
                               ForchheimerVelocity,
                               (GetPropType<TypeTag, Properties::GridGeometry>::GridView::dimension < GetPropType<TypeTag, Properties::GridGeometry>::GridView::dimensionworld)>
{};

template<class GridGeometry>
class TpfaForchheimersLawCacheFiller
{
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using Element = typename GridGeometry::GridView::template Codim<0>::Entity;
 
public:
    template<class FluxVariablesCache, class Problem, class ElementVolumeVariables, class FluxVariablesCacheFiller>
    static void fill(FluxVariablesCache& scvfFluxVarsCache,
                     const Problem& problem,
                     const Element& element,
                     const FVElementGeometry& fvGeometry,
                     const ElementVolumeVariables& elemVolVars,
                     const SubControlVolumeFace& scvf,
                     const FluxVariablesCacheFiller& fluxVarsCacheFiller)
    {
        scvfFluxVarsCache.updateAdvection(problem, element, fvGeometry, elemVolVars, scvf);
    }
};

template<class AdvectionType, class GridGeometry>
class TpfaForchheimersLawCache
{
    using Scalar = typename AdvectionType::Scalar;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using Element = typename GridGeometry::GridView::template Codim<0>::Entity;
    static constexpr int dimWorld = GridGeometry::GridView::dimensionworld;
    using DimWorldMatrix = Dune::FieldMatrix<Scalar, dimWorld, dimWorld>;
 
public:
    using Filler = TpfaForchheimersLawCacheFiller<GridGeometry>;
 
    template<class Problem, class ElementVolumeVariables>
    void updateAdvection(const Problem& problem,
                         const Element& element,
                         const FVElementGeometry& fvGeometry,
                         const ElementVolumeVariables& elemVolVars,
                         const SubControlVolumeFace &scvf)
    {
        tij_ = AdvectionType::calculateTransmissibility(problem, element, fvGeometry, elemVolVars, scvf);
        harmonicMeanSqrtK_ = AdvectionType::calculateHarmonicMeanSqrtPermeability(problem, elemVolVars, scvf);
    }
 
    const Scalar& advectionTij() const
    { return tij_; }
 
    const DimWorldMatrix& harmonicMeanSqrtPermeability() const
    { return harmonicMeanSqrtK_; }
 
private:
    Scalar tij_;
    DimWorldMatrix harmonicMeanSqrtK_;
};

template<class ScalarType, class GridGeometry, class ForchheimerVelocity>
class CCTpfaForchheimersLaw<ScalarType, GridGeometry, ForchheimerVelocity, /*isNetwork*/ false>
{
    using ThisType = CCTpfaForchheimersLaw<ScalarType, GridGeometry, ForchheimerVelocity, /*isNetwork*/ false>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using Extrusion = Extrusion_t<GridGeometry>;
    using GridView = typename GridGeometry::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
 
    using DimWorldVector = typename ForchheimerVelocity::DimWorldVector;
    using DimWorldMatrix = typename ForchheimerVelocity::DimWorldMatrix;
 
    using DarcysLaw = CCTpfaDarcysLaw<ScalarType, GridGeometry, /*isNetwork*/ false>;
 
  public:
    using Scalar = ScalarType;
 
    using DiscretizationMethod = DiscretizationMethods::CCTpfa;
    static constexpr DiscretizationMethod discMethod{};

    using Cache = TpfaForchheimersLawCache<ThisType, GridGeometry>;

    template<class Problem, class ElementVolumeVariables, class ElementFluxVarsCache>
    static Scalar flux(const Problem& problem,
                       const Element& element,
                       const FVElementGeometry& fvGeometry,
                       const ElementVolumeVariables& elemVolVars,
                       const SubControlVolumeFace& scvf,
                       int phaseIdx,
                       const ElementFluxVarsCache& elemFluxVarsCache)
    {
        // Get the volume flux based on Darcy's law. The value returned by this method needs to be multiplied with the
        // mobility (upwinding).
        Scalar darcyFlux = DarcysLaw::flux(problem, element, fvGeometry, elemVolVars, scvf, phaseIdx, elemFluxVarsCache);
        auto upwindTerm = [phaseIdx](const auto& volVars){ return volVars.mobility(phaseIdx); };
        DimWorldVector darcyVelocity = scvf.unitOuterNormal();
        darcyVelocity *= ForchheimerVelocity::UpwindScheme::apply(elemVolVars, scvf, upwindTerm, darcyFlux, phaseIdx);
        darcyVelocity /= Extrusion::area(scvf);
 
        const auto velocity = ForchheimerVelocity::velocity(fvGeometry,
                                                            elemVolVars,
                                                            scvf,
                                                            phaseIdx,
                                                            elemFluxVarsCache[scvf].harmonicMeanSqrtPermeability(),
                                                            darcyVelocity);
 
        Scalar flux = velocity * scvf.unitOuterNormal();
        flux *= Extrusion::area(scvf);
        return flux;
    }

    template<class Problem, class ElementVolumeVariables>
    static Scalar calculateTransmissibility(const Problem& problem,
                                            const Element& element,
                                            const FVElementGeometry& fvGeometry,
                                            const ElementVolumeVariables& elemVolVars,
                                            const SubControlVolumeFace& scvf)
    {
        return DarcysLaw::calculateTransmissibility(problem, element, fvGeometry, elemVolVars, scvf);
    }

    template<class Problem, class ElementVolumeVariables>
    static DimWorldMatrix calculateHarmonicMeanSqrtPermeability(const Problem& problem,
                                                                const ElementVolumeVariables& elemVolVars,
                                                                const SubControlVolumeFace& scvf)
    {
        return ForchheimerVelocity::calculateHarmonicMeanSqrtPermeability(problem, elemVolVars, scvf);
    }
};

template<class ScalarType, class GridGeometry, class ForchheimerVelocity>
class CCTpfaForchheimersLaw<ScalarType, GridGeometry, ForchheimerVelocity, /*isNetwork*/ true>
{
    static_assert(AlwaysFalse<ScalarType>::value, "Forchheimer not implemented for network grids");
};
 
} // end namespace Dumux
 
#endif