box/forchheimerslaw.hh

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#ifndef DUMUX_DISCRETIZATION_BOX_FORCHHEIMERS_LAW_HH
#define DUMUX_DISCRETIZATION_BOX_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/box/darcyslaw.hh>
#include <dumux/flux/facetensoraverage.hh>
 
namespace Dumux {
 
// forward declarations
template<class TypeTag, class ForchheimerVelocity, class DiscretizationMethod>
class ForchheimersLawImplementation;
 
template<class Scalar, class GridGeometry, class ForchheimerVelocity>
class BoxForchheimersLaw;
 
template <class TypeTag, class ForchheimerVelocity>
class ForchheimersLawImplementation<TypeTag, ForchheimerVelocity, DiscretizationMethods::Box>
: public BoxForchheimersLaw<GetPropType<TypeTag, Properties::Scalar>,
                            GetPropType<TypeTag, Properties::GridGeometry>,
                            ForchheimerVelocity>
{};
 
template<class ScalarType, class GridGeometry, class ForchheimerVelocity>
class BoxForchheimersLaw
{
    using ThisType = BoxForchheimersLaw<ScalarType, GridGeometry, ForchheimerVelocity>;
    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 = BoxDarcysLaw<ScalarType, GridGeometry>;
 
public:
    using Scalar = ScalarType;
 
    using DiscretizationMethod = DiscretizationMethods::Box;
    static constexpr DiscretizationMethod discMethod{};
 
    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)
    {
        const auto& fluxVarCache = elemFluxVarsCache[scvf];
        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
        const auto& insideVolVars = elemVolVars[insideScv];
        const auto& outsideVolVars = elemVolVars[outsideScv];
 
        auto insideK = insideVolVars.permeability();
        auto outsideK = outsideVolVars.permeability();
 
        // scale with correct extrusion factor
        insideK *= insideVolVars.extrusionFactor();
        outsideK *= outsideVolVars.extrusionFactor();
 
        const auto K = faceTensorAverage(insideK, outsideK, scvf.unitOuterNormal());
        static const bool enableGravity = getParamFromGroup<bool>(problem.paramGroup(), "Problem.EnableGravity");
 
        const auto& shapeValues = fluxVarCache.shapeValues();
 
        // evaluate gradP - rho*g at integration point
        DimWorldVector gradP(0.0);
        Scalar rho(0.0);
        for (auto&& scv : scvs(fvGeometry))
        {
            const auto& volVars = elemVolVars[scv];
 
            if (enableGravity)
                rho += volVars.density(phaseIdx)*shapeValues[scv.indexInElement()][0];
 
            // the global shape function gradient
            gradP.axpy(volVars.pressure(phaseIdx), fluxVarCache.gradN(scv.indexInElement()));
        }
 
        if (enableGravity)
            gradP.axpy(-rho, problem.spatialParams().gravity(scvf.center()));
 
        DimWorldVector darcyVelocity = mv(K, gradP);
        darcyVelocity *= -1;
 
        auto upwindTerm = [phaseIdx](const auto& volVars){ return volVars.mobility(phaseIdx); };
        darcyVelocity *= ForchheimerVelocity::UpwindScheme::multiplier(elemVolVars, scvf, upwindTerm, darcyVelocity*scvf.unitOuterNormal(), phaseIdx);
 
        const auto velocity = ForchheimerVelocity::velocity(fvGeometry,
                                                            elemVolVars,
                                                            scvf,
                                                            phaseIdx,
                                                            calculateHarmonicMeanSqrtPermeability(problem, elemVolVars, scvf),
                                                            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);
    }
};
 
} // end namespace Dumux
 
#endif