flux/staggered/freeflow/fickslaw.hh

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#ifndef DUMUX_DISCRETIZATION_STAGGERED_FICKS_LAW_HH
#define DUMUX_DISCRETIZATION_STAGGERED_FICKS_LAW_HH
 
#include <numeric>
#include <dune/common/fvector.hh>
 
#include <dumux/common/properties.hh>
#include <dumux/common/parameters.hh>
#include <dumux/common/math.hh>
 
#include <dumux/discretization/method.hh>
#include <dumux/discretization/extrusion.hh>
#include <dumux/flux/fluxvariablescaching.hh>
#include <dumux/flux/fickiandiffusioncoefficients.hh>
#include <dumux/flux/referencesystemformulation.hh>
 
 
namespace Dumux {
 
// forward declaration
template<class TypeTag, DiscretizationMethod discMethod, ReferenceSystemFormulation referenceSystem>
class FicksLawImplementation;
 
template <class TypeTag, ReferenceSystemFormulation referenceSystem>
class FicksLawImplementation<TypeTag, DiscretizationMethod::staggered, referenceSystem>
{
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using Extrusion = Extrusion_t<GridGeometry>;
    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
    using GridView = typename GridGeometry::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
    using Indices = typename ModelTraits::Indices;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
 
    static constexpr int numComponents = ModelTraits::numFluidComponents();
    static constexpr int numPhases = ModelTraits::numFluidPhases();
 
    using NumEqVector = Dune::FieldVector<Scalar, numComponents>;
 
    static_assert(ModelTraits::numFluidPhases() == 1, "Only one phase supported!");
 
public:
    // state the discretization method this implementation belongs to
    static const DiscretizationMethod discMethod = DiscretizationMethod::staggered;
    //return the reference system
    static constexpr ReferenceSystemFormulation referenceSystemFormulation()
    { return referenceSystem; }
 
    using Cache = FluxVariablesCaching::EmptyDiffusionCache;
 
    using DiffusionCoefficientsContainer = FickianDiffusionCoefficients<Scalar, numPhases, numComponents>;
 
    template<class Problem, class ElementVolumeVariables>
    static NumEqVector flux(const Problem& problem,
                            const Element& element,
                            const FVElementGeometry& fvGeometry,
                            const ElementVolumeVariables& elemVolVars,
                            const SubControlVolumeFace &scvf)
    {
        NumEqVector flux(0.0);
 
        // There is no diffusion over outflow boundaries (grad x == 0).
        // We assume that if an outflow BC is set for the first transported component, this
        // also holds for all other components.
        if (scvf.boundary() && problem.boundaryTypes(element, scvf).isOutflow(Indices::conti0EqIdx + 1))
            return flux;
 
        const int phaseIdx = 0;
 
        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];
        const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];
 
        const Scalar insideDistance = (insideScv.dofPosition() - scvf.ipGlobal()).two_norm();
        const Scalar insideDensity = massOrMolarDensity(insideVolVars, referenceSystem, phaseIdx);
 
        for (int compIdx = 0; compIdx < numComponents; ++compIdx)
        {
            if (compIdx == FluidSystem::getMainComponent(phaseIdx))
                continue;
 
            const Scalar massOrMoleFractionInside = massOrMoleFraction(insideVolVars, referenceSystem, phaseIdx, compIdx);
            const Scalar massOrMoleFractionOutside =  massOrMoleFraction(outsideVolVars, referenceSystem, phaseIdx, compIdx);
            const Scalar insideD = getEffectiveDiffusionCoefficient_(insideVolVars, phaseIdx, compIdx) * insideVolVars.extrusionFactor();
 
            if (scvf.boundary())
            {
                flux[compIdx] = insideDensity * insideD
                                * (massOrMoleFractionInside - massOrMoleFractionOutside) / insideDistance;
            }
            else
            {
                const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
                const Scalar outsideD = getEffectiveDiffusionCoefficient_(outsideVolVars, phaseIdx, compIdx)
                                      * outsideVolVars.extrusionFactor();
                const Scalar outsideDistance = (outsideScv.dofPosition() - scvf.ipGlobal()).two_norm();
                const Scalar outsideDensity = massOrMolarDensity(outsideVolVars, referenceSystem, phaseIdx);
 
                const Scalar avgDensity = 0.5*(insideDensity + outsideDensity);
                const Scalar avgD = harmonicMean(insideD, outsideD, insideDistance, outsideDistance);
 
                flux[compIdx] = avgDensity * avgD
                                * (massOrMoleFractionInside - massOrMoleFractionOutside) / (insideDistance + outsideDistance);
            }
        }
 
        // Fick's law (for binary systems) states that the net flux of mass within the bulk phase has to be zero:
        const Scalar cumulativeFlux = std::accumulate(flux.begin(), flux.end(), 0.0);
        flux[FluidSystem::getMainComponent(0)] = -cumulativeFlux;
 
        flux *= Extrusion::area(scvf);
 
        return flux;
    }
 
private:
    static Scalar getEffectiveDiffusionCoefficient_(const VolumeVariables& volVars, const int phaseIdx, const int compIdx)
    {
        return volVars.effectiveDiffusionCoefficient(phaseIdx, FluidSystem::getMainComponent(phaseIdx), compIdx);
    }
};
} // end namespace Dumux
 
#endif