flux/cctpfa/darcyslaw.hh

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#ifndef DUMUX_DISCRETIZATION_CC_TPFA_DARCYS_LAW_HH
#define DUMUX_DISCRETIZATION_CC_TPFA_DARCYS_LAW_HH
 
#include <dumux/common/math.hh>
#include <dumux/common/parameters.hh>
#include <dumux/common/properties.hh>
 
#include <dumux/discretization/method.hh>
#include <dumux/discretization/extrusion.hh>
#include <dumux/discretization/cellcentered/tpfa/computetransmissibility.hh>
 
namespace Dumux {
 
// forward declarations
template<class TypeTag, class DiscretizationMethod>
class DarcysLawImplementation;

template<class Scalar, class GridGeometry, bool isNetwork>
class CCTpfaDarcysLaw;

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

template<class GridGeometry>
class TpfaDarcysLawCacheFiller
{
    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 TpfaDarcysLawCache
{
    using Scalar = typename AdvectionType::Scalar;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using Element = typename GridGeometry::GridView::template Codim<0>::Entity;
 
public:
    using Filler = TpfaDarcysLawCacheFiller<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);
    }
 
    const Scalar& advectionTij() const
    { return tij_; }
 
private:
    Scalar tij_;
};

template<class ScalarType, class GridGeometry>
class CCTpfaDarcysLaw<ScalarType, GridGeometry, /*isNetwork*/ false>
{
    using ThisType = CCTpfaDarcysLaw<ScalarType, GridGeometry, /*isNetwork*/ false>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolume = typename GridGeometry::SubControlVolume;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using Extrusion = Extrusion_t<GridGeometry>;
    using GridView = typename GridGeometry::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
 
    static constexpr int dim = GridView::dimension;
    static constexpr int dimWorld = GridView::dimensionworld;
 
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
 
  public:
    using Scalar = ScalarType;
 
    using DiscretizationMethod = DiscretizationMethods::CCTpfa;
    static constexpr DiscretizationMethod discMethod{};

    using Cache = TpfaDarcysLawCache<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)
    {
        static const bool enableGravity = getParamFromGroup<bool>(problem.paramGroup(), "Problem.EnableGravity");
 
        const auto& fluxVarsCache = elemFluxVarsCache[scvf];
 
        // Get the inside and outside volume variables
        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
        const auto& insideVolVars = elemVolVars[insideScv];
        const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];
 
        if (enableGravity)
        {
            // do averaging for the density over all neighboring elements
            const auto rho = scvf.boundary() ? outsideVolVars.density(phaseIdx)
                                             : (insideVolVars.density(phaseIdx) + outsideVolVars.density(phaseIdx))*0.5;
 
            // Obtain inside and outside pressures
            const auto pInside = insideVolVars.pressure(phaseIdx);
            const auto pOutside = outsideVolVars.pressure(phaseIdx);
 
            const auto& tij = fluxVarsCache.advectionTij();
            const auto& g = problem.spatialParams().gravity(scvf.ipGlobal());

            const auto alpha_inside = vtmv(scvf.unitOuterNormal(), insideVolVars.permeability(), g)*insideVolVars.extrusionFactor();
 
            Scalar flux = tij*(pInside - pOutside) + rho*Extrusion::area(scvf)*alpha_inside;

            if (!scvf.boundary())
            {
                const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
                const auto outsideK = outsideVolVars.permeability();
                const auto outsideTi = fvGeometry.gridGeometry().isPeriodic()
                    ? computeTpfaTransmissibility(fvGeometry.flipScvf(scvf.index()), outsideScv, outsideK, outsideVolVars.extrusionFactor())
                    : -1.0*computeTpfaTransmissibility(scvf, outsideScv, outsideK, outsideVolVars.extrusionFactor());
                const auto alpha_outside = vtmv(scvf.unitOuterNormal(), outsideK, g)*outsideVolVars.extrusionFactor();
 
                flux -= rho*tij/outsideTi*(alpha_inside - alpha_outside);
            }
 
            return flux;
        }
        else
        {
            // Obtain inside and outside pressures
            const auto pInside = insideVolVars.pressure(phaseIdx);
            const auto pOutside = outsideVolVars.pressure(phaseIdx);
 
            // return flux
            return fluxVarsCache.advectionTij()*(pInside - pOutside);
        }
    }
 
    // The flux variables cache has to be bound to an element prior to flux calculations
    // During the binding, the transmissibility will be computed and stored using the method below.
    template<class Problem, class ElementVolumeVariables>
    static Scalar calculateTransmissibility(const Problem& problem,
                                            const Element& element,
                                            const FVElementGeometry& fvGeometry,
                                            const ElementVolumeVariables& elemVolVars,
                                            const SubControlVolumeFace& scvf)
    {
        Scalar tij;
 
        const auto insideScvIdx = scvf.insideScvIdx();
        const auto& insideScv = fvGeometry.scv(insideScvIdx);
        const auto& insideVolVars = elemVolVars[insideScvIdx];
 
        const Scalar ti = computeTpfaTransmissibility(scvf, insideScv,
                                                      getPermeability_(problem, insideVolVars, scvf.ipGlobal()),
                                                      insideVolVars.extrusionFactor());
 
        // on the boundary (dirichlet) we only need ti
        if (scvf.boundary())
            tij = Extrusion::area(scvf)*ti;
 
        // otherwise we compute a tpfa harmonic mean
        else
        {
            const auto outsideScvIdx = scvf.outsideScvIdx();
            // as we assemble fluxes from the neighbor to our element the outside index
            // refers to the scv of our element, so we use the scv method
            const auto& outsideScv = fvGeometry.scv(outsideScvIdx);
            const auto& outsideVolVars = elemVolVars[outsideScvIdx];
            const Scalar tj = fvGeometry.gridGeometry().isPeriodic()
                ? computeTpfaTransmissibility(fvGeometry.flipScvf(scvf.index()), outsideScv, getPermeability_(problem, outsideVolVars, scvf.ipGlobal()), outsideVolVars.extrusionFactor())
                : -1.0*computeTpfaTransmissibility(scvf, outsideScv, getPermeability_(problem, outsideVolVars, scvf.ipGlobal()), outsideVolVars.extrusionFactor());
 
            // harmonic mean (check for division by zero!)
            // TODO: This could lead to problems!? Is there a better way to do this?
            if (ti*tj <= 0.0)
                tij = 0;
            else
                tij = Extrusion::area(scvf)*(ti * tj)/(ti + tj);
        }
 
        return tij;
    }
 
private:
    template<class Problem, class VolumeVariables,
             std::enable_if_t<!Problem::SpatialParams::evaluatePermeabilityAtScvfIP(), int> = 0>
    static decltype(auto) getPermeability_(const Problem& problem,
                                           const VolumeVariables& volVars,
                                           const GlobalPosition& scvfIpGlobal)
    { return volVars.permeability(); }
 
    template<class Problem, class VolumeVariables,
             std::enable_if_t<Problem::SpatialParams::evaluatePermeabilityAtScvfIP(), int> = 0>
    static decltype(auto) getPermeability_(const Problem& problem,
                                           const VolumeVariables& volVars,
                                           const GlobalPosition& scvfIpGlobal)
    { return problem.spatialParams().permeabilityAtPos(scvfIpGlobal); }
};

template<class ScalarType, class GridGeometry>
class CCTpfaDarcysLaw<ScalarType, GridGeometry, /*isNetwork*/ true>
{
    using ThisType = CCTpfaDarcysLaw<ScalarType, GridGeometry, /*isNetwork*/ true>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolume = typename GridGeometry::SubControlVolume;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using Extrusion = Extrusion_t<GridGeometry>;
    using GridView = typename GridGeometry::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
 
    static constexpr int dim = GridView::dimension;
    static constexpr int dimWorld = GridView::dimensionworld;
 
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
 
public:
    using Scalar = ScalarType;
 
    using DiscretizationMethod = DiscretizationMethods::CCTpfa;
    static constexpr DiscretizationMethod discMethod{};

    using Cache = TpfaDarcysLawCache<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)
    {
        static const bool gravity = getParamFromGroup<bool>(problem.paramGroup(), "Problem.EnableGravity");
 
        const auto& fluxVarsCache = elemFluxVarsCache[scvf];
 
        // Get the inside and outside volume variables
        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
        const auto& insideVolVars = elemVolVars[insideScv];
        const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];
 
        if (gravity)
        {
            // do averaging for the density over all neighboring elements
            const auto rho = [&]()
            {
                // boundaries
                if (scvf.boundary())
                    return outsideVolVars.density(phaseIdx);
 
                // inner faces with two neighboring elements
                else if (scvf.numOutsideScvs() == 1)
                    return (insideVolVars.density(phaseIdx) + outsideVolVars.density(phaseIdx))*0.5;
 
                // inner faces in networks (general case)
                else
                {
                    Scalar rho(insideVolVars.density(phaseIdx));
                    for (unsigned int i = 0; i < scvf.numOutsideScvs(); ++i)
                    {
                        const auto outsideScvIdx = scvf.outsideScvIdx(i);
                        const auto& outsideVolVars = elemVolVars[outsideScvIdx];
                        rho += outsideVolVars.density(phaseIdx);
                    }
                    return rho/(scvf.numOutsideScvs()+1);
                }
            }();
 
            const auto& tij = fluxVarsCache.advectionTij();
            const auto& g = problem.spatialParams().gravity(scvf.ipGlobal());
 
            // Obtain inside and outside pressures
            const auto pInside = insideVolVars.pressure(phaseIdx);
            const auto pOutside = [&]()
            {
                // Dirichlet boundaries and inner faces with one neighbor
                if (scvf.numOutsideScvs() == 1)
                    return outsideVolVars.pressure(phaseIdx);
 
                // inner faces in networks (general case)
                else
                {
                    Scalar sumTi(tij);
                    Scalar sumPTi(tij*pInside);
 
                    // add inside gravitational contribution
                    sumPTi += rho*Extrusion::area(scvf)
                              *insideVolVars.extrusionFactor()
                              *vtmv(scvf.unitOuterNormal(), insideVolVars.permeability(), g);
 
                    for (unsigned int i = 0; i < scvf.numOutsideScvs(); ++i)
                    {
                        const auto outsideScvIdx = scvf.outsideScvIdx(i);
                        const auto& flippedScvf = fvGeometry.flipScvf(scvf.index(), i);
                        const auto& outsideVolVars = elemVolVars[outsideScvIdx];
                        const auto& outsideFluxVarsCache = elemFluxVarsCache[flippedScvf];
                        sumTi += outsideFluxVarsCache.advectionTij();
                        sumPTi += outsideFluxVarsCache.advectionTij()*outsideVolVars.pressure(phaseIdx);
 
                        // add outside gravitational contribution
                        sumPTi += rho*Extrusion::area(scvf)
                                  *outsideVolVars.extrusionFactor()
                                  *vtmv(flippedScvf.unitOuterNormal(), outsideVolVars.permeability(), g);
                    }
                    return sumPTi/sumTi;
                }
            }();

            const auto alpha_inside = vtmv(scvf.unitOuterNormal(), insideVolVars.permeability(), g)*insideVolVars.extrusionFactor();
 
            Scalar flux = tij*(pInside - pOutside) + Extrusion::area(scvf)*rho*alpha_inside;

            if (!scvf.boundary() && scvf.numOutsideScvs() == 1)
            {
                const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
                const auto& outsideScvf = fvGeometry.flipScvf(scvf.index());
                const auto outsideK = outsideVolVars.permeability();
                const auto outsideTi = computeTpfaTransmissibility(outsideScvf, outsideScv, outsideK, outsideVolVars.extrusionFactor());
                const auto alpha_outside = vtmv(outsideScvf.unitOuterNormal(), outsideK, g)*outsideVolVars.extrusionFactor();
 
                flux -= rho*tij/outsideTi*(alpha_inside + alpha_outside);
            }
 
            return flux;
        }
        else
        {
            // Obtain inside and outside pressures
            const auto pInside = insideVolVars.pressure(phaseIdx);
            const auto pOutside = [&]()
            {
                // Dirichlet boundaries and inner faces with two neighboring elements
                if (scvf.numOutsideScvs() <= 1)
                    return outsideVolVars.pressure(phaseIdx);
 
                // inner faces in networks (general case)
                else
                {
                    const auto& insideFluxVarsCache = elemFluxVarsCache[scvf];
                    Scalar sumTi(insideFluxVarsCache.advectionTij());
                    Scalar sumPTi(insideFluxVarsCache.advectionTij()*pInside);
 
                    for (unsigned int i = 0; i < scvf.numOutsideScvs(); ++i)
                    {
                        const auto outsideScvIdx = scvf.outsideScvIdx(i);
                        const auto& flippedScvf = fvGeometry.flipScvf(scvf.index(), i);
                        const auto& outsideVolVars = elemVolVars[outsideScvIdx];
                        const auto& outsideFluxVarsCache = elemFluxVarsCache[flippedScvf];
                        sumTi += outsideFluxVarsCache.advectionTij();
                        sumPTi += outsideFluxVarsCache.advectionTij()*outsideVolVars.pressure(phaseIdx);
                    }
                    return sumPTi/sumTi;
                }
            }();
 
            // return flux
            return fluxVarsCache.advectionTij()*(pInside - pOutside);
        }
    }
 
    // The flux variables cache has to be bound to an element prior to flux calculations
    // During the binding, the transmissibility will be computed and stored using the method below.
    template<class Problem, class ElementVolumeVariables>
    static Scalar calculateTransmissibility(const Problem& problem,
                                            const Element& element,
                                            const FVElementGeometry& fvGeometry,
                                            const ElementVolumeVariables& elemVolVars,
                                            const SubControlVolumeFace& scvf)
    {
        Scalar tij;
 
        const auto insideScvIdx = scvf.insideScvIdx();
        const auto& insideScv = fvGeometry.scv(insideScvIdx);
        const auto& insideVolVars = elemVolVars[insideScvIdx];
 
        const Scalar ti = computeTpfaTransmissibility(scvf, insideScv,
                                                      getPermeability_(problem, insideVolVars, scvf.ipGlobal()),
                                                      insideVolVars.extrusionFactor());
 
        // for the boundary (dirichlet) or at branching points we only need ti
        if (scvf.boundary() || scvf.numOutsideScvs() > 1)
            tij = Extrusion::area(scvf)*ti;
 
        // otherwise we compute a tpfa harmonic mean
        else
        {
            const auto outsideScvIdx = scvf.outsideScvIdx();
            // as we assemble fluxes from the neighbor to our element the outside index
            // refers to the scv of our element, so we use the scv method
            const auto& outsideScv = fvGeometry.scv(outsideScvIdx);
            const auto& outsideVolVars = elemVolVars[outsideScvIdx];
            const Scalar tj = computeTpfaTransmissibility(fvGeometry.flipScvf(scvf.index()), outsideScv,
                                                          getPermeability_(problem, outsideVolVars, scvf.ipGlobal()),
                                                          outsideVolVars.extrusionFactor());
 
            // harmonic mean (check for division by zero!)
            // TODO: This could lead to problems!? Is there a better way to do this?
            if (ti*tj <= 0.0)
                tij = 0;
            else
                tij = Extrusion::area(scvf)*(ti * tj)/(ti + tj);
        }
 
        return tij;
    }
 
private:
    template<class Problem, class VolumeVariables,
             std::enable_if_t<!Problem::SpatialParams::evaluatePermeabilityAtScvfIP(), int> = 0>
    static decltype(auto) getPermeability_(const Problem& problem,
                                           const VolumeVariables& volVars,
                                           const GlobalPosition& scvfIpGlobal)
    { return volVars.permeability(); }
 
    template<class Problem, class VolumeVariables,
             std::enable_if_t<Problem::SpatialParams::evaluatePermeabilityAtScvfIP(), int> = 0>
    static decltype(auto) getPermeability_(const Problem& problem,
                                           const VolumeVariables& volVars,
                                           const GlobalPosition& scvfIpGlobal)
    { return problem.spatialParams().permeabilityAtPos(scvfIpGlobal); }
};
 
} // end namespace Dumux
 
#endif