box/dispersionflux.hh

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#ifndef DUMUX_DISCRETIZATION_BOX_DISPERSION_FLUX_HH
#define DUMUX_DISCRETIZATION_BOX_DISPERSION_FLUX_HH
 
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
 
#include <dumux/common/math.hh>
#include <dumux/common/properties.hh>
#include <dumux/discretization/method.hh>
#include <dumux/discretization/extrusion.hh>
#include <dumux/flux/traits.hh>
#include <dumux/flux/referencesystemformulation.hh>
 
namespace Dumux {
 
// forward declaration
template<class TypeTag, class DiscretizationMethod, ReferenceSystemFormulation referenceSystem>
class DispersionFluxImplementation;
 
template <class TypeTag, ReferenceSystemFormulation referenceSystem>
class DispersionFluxImplementation<TypeTag, DiscretizationMethods::Box, referenceSystem>
{
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolume = typename GridGeometry::SubControlVolume;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using Extrusion = Extrusion_t<GridGeometry>;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using GridFluxVariablesCache = GetPropType<TypeTag, Properties::GridFluxVariablesCache>;
    using ElementFluxVariablesCache = typename GridFluxVariablesCache::LocalView;
    using FluxVarCache = typename GridFluxVariablesCache::FluxVariablesCache;
    using FluxVariables = GetPropType<TypeTag, Properties::FluxVariables>;
    using FluxTraits = typename Dumux::FluxTraits<FluxVariables>;
    using BalanceEqOpts = GetPropType<TypeTag, Properties::BalanceEqOpts>;
    using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
    using Indices = typename ModelTraits::Indices;
 
    enum { dim = GridView::dimension} ;
    enum { dimWorld = GridView::dimensionworld} ;
    enum
    {
        numPhases = ModelTraits::numFluidPhases(),
        numComponents = ModelTraits::numFluidComponents()
    };
 
    using DimWorldMatrix = Dune::FieldMatrix<Scalar, dimWorld, dimWorld>;
    using ComponentFluxVector = Dune::FieldVector<Scalar, numComponents>;
    using HeatFluxScalar = Scalar;
 
    static constexpr bool stationaryVelocityField = FluxTraits::hasStationaryVelocityField();
 
public:
 
    //return the reference system
    static constexpr ReferenceSystemFormulation referenceSystemFormulation()
    { return referenceSystem; }
 
    static ComponentFluxVector compositionalDispersionFlux(const Problem& problem,
                                                           const Element& element,
                                                           const FVElementGeometry& fvGeometry,
                                                           const ElementVolumeVariables& elemVolVars,
                                                           const SubControlVolumeFace& scvf,
                                                           const int phaseIdx,
                                                           const ElementFluxVariablesCache& elemFluxVarsCache)
    {
        ComponentFluxVector componentFlux(0.0);
 
        const auto& fluxVarsCache = elemFluxVarsCache[scvf];
        const auto& shapeValues = fluxVarsCache.shapeValues();
 
        // density interpolation
        Scalar rhoMassOrMole(0.0);
        for (auto&& scv : scvs(fvGeometry))
        {
            const auto rho = massOrMolarDensity(elemVolVars[scv], referenceSystem, phaseIdx);
            rhoMassOrMole += rho * shapeValues[scv.indexInElement()][0];
        }
 
        for (int compIdx = 0; compIdx < numComponents; compIdx++)
        {
            // collect the dispersion tensor, the fluxVarsCache and the shape values
            const auto& dispersionTensor =
                ModelTraits::CompositionalDispersionModel::compositionalDispersionTensor(problem, scvf, fvGeometry,
                                                                                         elemVolVars, elemFluxVarsCache,
                                                                                         phaseIdx, compIdx);
 
            // the mole/mass fraction gradient
            Dune::FieldVector<Scalar, dimWorld> gradX(0.0);
            for (auto&& scv : scvs(fvGeometry))
            {
                const auto x = massOrMoleFraction(elemVolVars[scv], referenceSystem, phaseIdx, compIdx);
                gradX.axpy(x, fluxVarsCache.gradN(scv.indexInElement()));
            }
 
            // compute the dispersion flux
            componentFlux[compIdx] = -1.0 * rhoMassOrMole * vtmv(scvf.unitOuterNormal(), dispersionTensor, gradX) * scvf.area();
            if (BalanceEqOpts::mainComponentIsBalanced(phaseIdx) && !FluidSystem::isTracerFluidSystem())
                componentFlux[phaseIdx] -= componentFlux[compIdx];
        }
        return componentFlux;
    }
 
    static HeatFluxScalar thermalDispersionFlux(const Problem& problem,
                                                const Element& element,
                                                const FVElementGeometry& fvGeometry,
                                                const ElementVolumeVariables& elemVolVars,
                                                const SubControlVolumeFace& scvf,
                                                const int phaseIdx,
                                                const ElementFluxVariablesCache& elemFluxVarsCache)
    {
        // collect the dispersion tensor
        const auto& dispersionTensor =
            ModelTraits::ThermalDispersionModel::thermalDispersionTensor(problem, scvf, fvGeometry,
                                                                         elemVolVars, elemFluxVarsCache,
                                                                         phaseIdx);
        // compute the temperature gradient with the shape functions
        const auto& fluxVarsCache = elemFluxVarsCache[scvf];
        Dune::FieldVector<Scalar, GridView::dimensionworld> gradTemp(0.0);
        for (auto&& scv : scvs(fvGeometry))
            gradTemp.axpy(elemVolVars[scv].temperature(), fluxVarsCache.gradN(scv.indexInElement()));
 
        // compute the heat conduction flux
        return -1.0*vtmv(scvf.unitOuterNormal(), dispersionTensor, gradTemp)*Extrusion::area(fvGeometry, scvf);
    }
 
};
 
} // end namespace Dumux
 
#endif