flux/cvfe/darcyslaw.hh

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
//
// SPDX-FileCopyrightText: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
// SPDX-License-Identifier: GPL-3.0-or-later
//
#ifndef DUMUX_DISCRETIZATION_CVFE_DARCYS_LAW_HH
#define DUMUX_DISCRETIZATION_CVFE_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/flux/facetensoraverage.hh>
#include <dumux/flux/gravitytermdensity.hh>
 
namespace Dumux {

template<class Scalar, class GridGeometry, class GravityTermDensity = PhaseDensityInGravityTerm>
class CVFEDarcysLaw
{
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolumeFace = typename FVElementGeometry::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;
 
public:

    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,
                       const int phaseIdx,
                       const ElementFluxVarsCache& elemFluxVarCache)
    {
        const auto& fluxVarCache = elemFluxVarCache[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());
        const auto gradPotential = potentialGradient(problem, fvGeometry, elemVolVars, scvf, phaseIdx, fluxVarCache);
 
        // apply the permeability and return the flux
        return -1.0*vtmv(scvf.unitOuterNormal(), K, gradPotential)*Extrusion::area(fvGeometry, scvf);
    }

    template<class Problem, class ElementVolumeVariables, class FluxVarCache>
    static Dune::FieldVector<Scalar, dimWorld> potentialGradient(const Problem& problem,
                                                                  const FVElementGeometry& fvGeometry,
                                                                  const ElementVolumeVariables& elemVolVars,
                                                                  const SubControlVolumeFace& scvf,
                                                                  const int phaseIdx,
                                                                  const FluxVarCache& fluxVarCache)
    {
        static const bool enableGravity = getParamFromGroup<bool>(problem.paramGroup(), "Problem.EnableGravity");
 
        const auto& shapeValues = fluxVarCache.shapeValues();
 
        Dune::FieldVector<Scalar, dimWorld> gradP(0.0);
        Scalar rho(0.0);
        for (auto&& scv : scvs(fvGeometry))
        {
            const auto& volVars = elemVolVars[scv];
 
            if (enableGravity)
                rho += GravityTermDensity::density(problem, volVars, 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()));
 
        return gradP;
    }
 
    // compute transmissibilities ti for analytical Jacobians
    template<class Problem, class ElementVolumeVariables, class FluxVarCache>
    static std::vector<Scalar> calculateTransmissibilities(const Problem& problem,
                                                           const Element& element,
                                                           const FVElementGeometry& fvGeometry,
                                                           const ElementVolumeVariables& elemVolVars,
                                                           const SubControlVolumeFace& scvf,
                                                           const FluxVarCache& fluxVarCache)
    {
        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());
 
        std::vector<Scalar> ti(fvGeometry.numScv());
        for (const auto& scv : scvs(fvGeometry))
            ti[scv.indexInElement()] =
                -1.0*Extrusion::area(fvGeometry, scvf)*vtmv(scvf.unitOuterNormal(), K, fluxVarCache.gradN(scv.indexInElement()));
 
        return ti;
    }
};
 
// forward declaration
template<class TypeTag, class DiscretizationMethod>
class DarcysLawImplementation;

template<class TypeTag, class DM>
class DarcysLawImplementation<TypeTag, DiscretizationMethods::CVFE<DM>>
: public CVFEDarcysLaw<GetPropType<TypeTag, Properties::Scalar>, GetPropType<TypeTag, Properties::GridGeometry>>
{};
 
} // end namespace Dumux
 
#endif