porousmediumflow/richards/localresidual.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-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
// SPDX-License-Identifier: GPL-3.0-or-later
//
#ifndef DUMUX_RICHARDS_LOCAL_RESIDUAL_HH
#define DUMUX_RICHARDS_LOCAL_RESIDUAL_HH
 
#include <dumux/common/properties.hh>
#include <dumux/common/parameters.hh>
#include <dumux/common/typetraits/typetraits.hh>
#include <dumux/common/numeqvector.hh>
#include <dumux/discretization/method.hh>
#include <dumux/discretization/extrusion.hh>
#include <dumux/flux/referencesystemformulation.hh>
 
namespace Dumux::Detail {
// helper structs and functions detecting if the user-defined problem class
// implements addRobinFluxDerivatives
template <typename T, typename ...Ts>
using RobinDerivDetector = decltype(std::declval<T>().addRobinFluxDerivatives(std::declval<Ts>()...));
 
template<class T, typename ...Args>
static constexpr bool hasAddRobinFluxDerivatives()
{ return Dune::Std::is_detected<RobinDerivDetector, T, Args...>::value; }
 
} // end namespace Dumux::Detail
 
namespace Dumux {
 
template<class TypeTag>
class RichardsLocalResidual : public GetPropType<TypeTag, Properties::BaseLocalResidual>
{
    using Implementation = GetPropType<TypeTag, Properties::LocalResidual>;
 
    using ParentType = GetPropType<TypeTag, Properties::BaseLocalResidual>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
    using NumEqVector = Dumux::NumEqVector<GetPropType<TypeTag, Properties::PrimaryVariables>>;
    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using FluxVariables = GetPropType<TypeTag, Properties::FluxVariables>;
    using ElementFluxVariablesCache = typename GetPropType<TypeTag, Properties::GridFluxVariablesCache>::LocalView;
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using Extrusion = Extrusion_t<GridGeometry>;
    using SubControlVolume = typename GridGeometry::SubControlVolume;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using GridView = typename GridGeometry::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
    using EnergyLocalResidual = GetPropType<TypeTag, Properties::EnergyLocalResidual>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
    // first index for the mass balance
    enum { conti0EqIdx = Indices::conti0EqIdx };
 
    // checks if the fluid system uses the Richards model index convention
    static constexpr auto fsCheck = GetPropType<TypeTag, Properties::ModelTraits>::checkFluidSystem(FluidSystem{});
 
    // phase & component indices
    static constexpr auto liquidPhaseIdx = FluidSystem::phase0Idx;
    static constexpr auto gasPhaseIdx = FluidSystem::phase1Idx;
    static constexpr auto liquidCompIdx = FluidSystem::comp0Idx;
 
    struct InvalidElemSol
    {
        template<class Index>
        double operator[] (const Index i) const
        { static_assert(AlwaysFalse<Index>::value, "Solution-dependent material parameters not supported with analytical differentiation"); return 0.0; }
    };
 
public:
    using ParentType::ParentType;
 
    NumEqVector computeStorage(const Problem& problem,
                               const SubControlVolume& scv,
                               const VolumeVariables& volVars) const
    {
        // partial time derivative of the phase mass
        NumEqVector storage(0.0);
        storage[conti0EqIdx] = volVars.porosity()
                               * volVars.density(liquidPhaseIdx)
                               * volVars.saturation(liquidPhaseIdx);
 
        EnergyLocalResidual::fluidPhaseStorage(storage, scv, volVars, liquidPhaseIdx);
        EnergyLocalResidual::fluidPhaseStorage(storage, scv, volVars, gasPhaseIdx);
        EnergyLocalResidual::solidPhaseStorage(storage, scv, volVars);
 
        return storage;
    }
 
 
    NumEqVector computeFlux(const Problem& problem,
                            const Element& element,
                            const FVElementGeometry& fvGeometry,
                            const ElementVolumeVariables& elemVolVars,
                            const SubControlVolumeFace& scvf,
                            const ElementFluxVariablesCache& elemFluxVarsCache) const
    {
        FluxVariables fluxVars;
        fluxVars.init(problem, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache);
 
        NumEqVector flux(0.0);
        // the physical quantities for which we perform upwinding
        auto upwindTerm = [](const auto& volVars)
                          { return volVars.density(liquidPhaseIdx)*volVars.mobility(liquidPhaseIdx); };
 
        flux[conti0EqIdx] = fluxVars.advectiveFlux(liquidPhaseIdx, upwindTerm);
 
        EnergyLocalResidual::heatConvectionFlux(flux, fluxVars, liquidPhaseIdx);
 
        EnergyLocalResidual::heatConductionFlux(flux, fluxVars);
 
        return flux;
    }
 
    template<class PartialDerivativeMatrix>
    void addStorageDerivatives(PartialDerivativeMatrix& partialDerivatives,
                               const Problem& problem,
                               const Element& element,
                               const FVElementGeometry& fvGeometry,
                               const VolumeVariables& curVolVars,
                               const SubControlVolume& scv) const
    {
        static_assert(!FluidSystem::isCompressible(0),
                      "richards/localresidual.hh: Analytic Jacobian only supports incompressible fluids!");
 
        const auto poreVolume = Extrusion::volume(fvGeometry, scv)*curVolVars.porosity()*curVolVars.extrusionFactor();
        static const auto rho = curVolVars.density(0);
 
        // partial derivative of storage term w.r.t. p_w
        // d(Sw*rho*phi*V/dt)/dpw = rho*phi*V/dt*dsw/dpw = rho*phi*V/dt*dsw/dpc*dpc/dpw = -rho*phi*V/dt*dsw/dpc
        const auto fluidMatrixInteraction = problem.spatialParams().fluidMatrixInteraction(element, scv, InvalidElemSol{});
        partialDerivatives[conti0EqIdx][0] += -rho*poreVolume/this->timeLoop().timeStepSize()*fluidMatrixInteraction.dsw_dpc(curVolVars.capillaryPressure());
    }
 
    template<class PartialDerivativeMatrix>
    void addSourceDerivatives(PartialDerivativeMatrix& partialDerivatives,
                              const Problem& problem,
                              const Element& element,
                              const FVElementGeometry& fvGeometry,
                              const VolumeVariables& curVolVars,
                              const SubControlVolume& scv) const
    { /* TODO maybe forward to problem for the user to implement the source derivatives?*/ }
 
    template<class PartialDerivativeMatrices, class T = TypeTag>
    std::enable_if_t<GetPropType<T, Properties::GridGeometry>::discMethod == DiscretizationMethods::cctpfa, void>
    addFluxDerivatives(PartialDerivativeMatrices& derivativeMatrices,
                       const Problem& problem,
                       const Element& element,
                       const FVElementGeometry& fvGeometry,
                       const ElementVolumeVariables& curElemVolVars,
                       const ElementFluxVariablesCache& elemFluxVarsCache,
                       const SubControlVolumeFace& scvf) const
    {
        static_assert(!FluidSystem::isCompressible(0),
                      "richards/localresidual.hh: Analytic Jacobian only supports incompressible fluids!");
        static_assert(FluidSystem::viscosityIsConstant(0),
                      "richards/localresidual.hh: Analytic Jacobian only supports fluids with constant viscosity!");
 
        // get references to the two participating vol vars & parameters
        const auto insideScvIdx = scvf.insideScvIdx();
        const auto outsideScvIdx = scvf.outsideScvIdx();
        const auto outsideElement = fvGeometry.gridGeometry().element(outsideScvIdx);
        const auto& insideScv = fvGeometry.scv(insideScvIdx);
        const auto& outsideScv = fvGeometry.scv(outsideScvIdx);
        const auto& insideVolVars = curElemVolVars[insideScvIdx];
        const auto& outsideVolVars = curElemVolVars[outsideScvIdx];
 
        // some quantities to be reused (rho & mu are constant and thus equal for all cells)
        static const auto rho = insideVolVars.density(0);
        static const auto mu = insideVolVars.viscosity(0);
        static const auto rho_mu = rho/mu;
 
        // upwind term
        // evaluate the current wetting phase Darcy flux and resulting upwind weights
        using AdvectionType = GetPropType<TypeTag, Properties::AdvectionType>;
        static const Scalar upwindWeight = getParamFromGroup<Scalar>(problem.paramGroup(), "Flux.UpwindWeight");
        const auto flux = AdvectionType::flux(problem, element, fvGeometry, curElemVolVars, scvf, 0, elemFluxVarsCache);
        const auto insideWeight = std::signbit(flux) ? (1.0 - upwindWeight) : upwindWeight;
        const auto outsideWeight = 1.0 - insideWeight;
        const auto upwindTerm = rho*insideVolVars.mobility(0)*insideWeight + rho*outsideVolVars.mobility(0)*outsideWeight;
 
        const auto insideFluidMatrixInteraction = problem.spatialParams().fluidMatrixInteraction(element, insideScv, InvalidElemSol{});
        const auto outsideFluidMatrixInteraction = problem.spatialParams().fluidMatrixInteraction(outsideElement, outsideScv, InvalidElemSol{});
 
        // material law derivatives
        const auto insideSw = insideVolVars.saturation(0);
        const auto outsideSw = outsideVolVars.saturation(0);
        const auto insidePc = insideVolVars.capillaryPressure();
        const auto outsidePc = outsideVolVars.capillaryPressure();
        const auto dkrw_dsw_inside = insideFluidMatrixInteraction.dkrw_dsw(insideSw);
        const auto dkrw_dsw_outside = outsideFluidMatrixInteraction.dkrw_dsw(outsideSw);
        const auto dsw_dpw_inside = -insideFluidMatrixInteraction.dsw_dpc(insidePc);
        const auto dsw_dpw_outside = -outsideFluidMatrixInteraction.dsw_dpc(outsidePc);
 
        // the transmissibility
        const auto tij = elemFluxVarsCache[scvf].advectionTij();
 
        // get references to the two participating derivative matrices
        auto& dI_dI = derivativeMatrices[insideScvIdx];
        auto& dI_dJ = derivativeMatrices[outsideScvIdx];
 
        // partial derivative of the wetting phase flux w.r.t. pw
        dI_dI[conti0EqIdx][0] += tij*upwindTerm + rho_mu*flux*insideWeight*dkrw_dsw_inside*dsw_dpw_inside;
        dI_dJ[conti0EqIdx][0] += -tij*upwindTerm + rho_mu*flux*outsideWeight*dkrw_dsw_outside*dsw_dpw_outside;
    }
 
    template<class JacobianMatrix, class T = TypeTag>
    std::enable_if_t<GetPropType<T, Properties::GridGeometry>::discMethod == DiscretizationMethods::box, void>
    addFluxDerivatives(JacobianMatrix& A,
                       const Problem& problem,
                       const Element& element,
                       const FVElementGeometry& fvGeometry,
                       const ElementVolumeVariables& curElemVolVars,
                       const ElementFluxVariablesCache& elemFluxVarsCache,
                       const SubControlVolumeFace& scvf) const
    {
        static_assert(!FluidSystem::isCompressible(0),
                      "richards/localresidual.hh: Analytic Jacobian only supports incompressible fluids!");
        static_assert(FluidSystem::viscosityIsConstant(0),
                      "richards/localresidual.hh: Analytic Jacobian only supports fluids with constant viscosity!");
 
        // get references to the two participating vol vars & parameters
        const auto insideScvIdx = scvf.insideScvIdx();
        const auto outsideScvIdx = scvf.outsideScvIdx();
        const auto& insideScv = fvGeometry.scv(insideScvIdx);
        const auto& outsideScv = fvGeometry.scv(outsideScvIdx);
        const auto& insideVolVars = curElemVolVars[insideScvIdx];
        const auto& outsideVolVars = curElemVolVars[outsideScvIdx];
 
        // some quantities to be reused (rho & mu are constant and thus equal for all cells)
        static const auto rho = insideVolVars.density(0);
        static const auto mu = insideVolVars.viscosity(0);
        static const auto rho_mu = rho/mu;
 
        // upwind term
        // evaluate the current wetting phase Darcy flux and resulting upwind weights
        using AdvectionType = GetPropType<TypeTag, Properties::AdvectionType>;
        static const Scalar upwindWeight = getParamFromGroup<Scalar>(problem.paramGroup(), "Flux.UpwindWeight");
        const auto flux = AdvectionType::flux(problem, element, fvGeometry, curElemVolVars, scvf, 0, elemFluxVarsCache);
        const auto insideWeight = std::signbit(flux) ? (1.0 - upwindWeight) : upwindWeight;
        const auto outsideWeight = 1.0 - insideWeight;
        const auto upwindTerm = rho*insideVolVars.mobility(0)*insideWeight + rho*outsideVolVars.mobility(0)*outsideWeight;
 
        const auto insideFluidMatrixInteraction = problem.spatialParams().fluidMatrixInteraction(element, insideScv, InvalidElemSol{});
        const auto outsideFluidMatrixInteraction = problem.spatialParams().fluidMatrixInteraction(element, outsideScv, InvalidElemSol{});
 
        // material law derivatives
        const auto insideSw = insideVolVars.saturation(0);
        const auto outsideSw = outsideVolVars.saturation(0);
        const auto insidePc = insideVolVars.capillaryPressure();
        const auto outsidePc = outsideVolVars.capillaryPressure();
        const auto dkrw_dsw_inside = insideFluidMatrixInteraction.dkrw_dsw(insideSw);
        const auto dkrw_dsw_outside = outsideFluidMatrixInteraction.dkrw_dsw(outsideSw);
        const auto dsw_dpw_inside = -insideFluidMatrixInteraction.dsw_dpc(insidePc);
        const auto dsw_dpw_outside = -outsideFluidMatrixInteraction.dsw_dpc(outsidePc);
 
        // so far it was the same as for tpfa
        // the transmissibilities (flux derivatives with respect to all pw-dofs on the element)
        const auto ti = AdvectionType::calculateTransmissibilities(
            problem, element, fvGeometry, curElemVolVars, scvf, elemFluxVarsCache[scvf]
        );
 
        // get the rows of the jacobian matrix for the inside/outside scv
        auto& dI_dJ_inside = A[insideScv.dofIndex()];
        auto& dI_dJ_outside = A[outsideScv.dofIndex()];
 
        // add the partial derivatives w.r.t all scvs in the element
        for (const auto& scvJ : scvs(fvGeometry))
        {
            // the transmissibily associated with the scvJ
            const auto& tj = ti[scvJ.indexInElement()];
            const auto globalJ = scvJ.dofIndex();
 
            // partial derivative of the wetting phase flux w.r.t. p_w
            dI_dJ_inside[globalJ][conti0EqIdx][0] += tj*upwindTerm;
            dI_dJ_outside[globalJ][conti0EqIdx][0] += -tj*upwindTerm;
        }
 
        const auto upwindContributionInside = rho_mu*flux*insideWeight*dkrw_dsw_inside*dsw_dpw_inside;
        const auto upwindContributionOutside = rho_mu*flux*outsideWeight*dkrw_dsw_outside*dsw_dpw_outside;
 
        // additional contribution of the upwind term only for inside and outside dof
        A[insideScv.dofIndex()][insideScv.dofIndex()][conti0EqIdx][0] += upwindContributionInside;
        A[insideScv.dofIndex()][outsideScv.dofIndex()][conti0EqIdx][0] += upwindContributionOutside;
 
        A[outsideScv.dofIndex()][insideScv.dofIndex()][conti0EqIdx][0] -= upwindContributionInside;
        A[outsideScv.dofIndex()][outsideScv.dofIndex()][conti0EqIdx][0] -= upwindContributionOutside;
    }
 
    template<class PartialDerivativeMatrices>
    void addCCDirichletFluxDerivatives(PartialDerivativeMatrices& derivativeMatrices,
                                       const Problem& problem,
                                       const Element& element,
                                       const FVElementGeometry& fvGeometry,
                                       const ElementVolumeVariables& curElemVolVars,
                                       const ElementFluxVariablesCache& elemFluxVarsCache,
                                       const SubControlVolumeFace& scvf) const
    {
        static_assert(!FluidSystem::isCompressible(0),
                      "richards/localresidual.hh: Analytic Jacobian only supports incompressible fluids!");
        static_assert(FluidSystem::viscosityIsConstant(0),
                      "richards/localresidual.hh: Analytic Jacobian only supports fluids with constant viscosity!");
 
 
        // get references to the two participating vol vars & parameters
        const auto insideScvIdx = scvf.insideScvIdx();
        const auto& insideScv = fvGeometry.scv(insideScvIdx);
        const auto& insideVolVars = curElemVolVars[insideScvIdx];
        const auto& outsideVolVars = curElemVolVars[scvf.outsideScvIdx()];
        const auto insideFluidMatrixInteraction = problem.spatialParams().fluidMatrixInteraction(element, insideScv, InvalidElemSol{});
 
        // some quantities to be reused (rho & mu are constant and thus equal for all cells)
        static const auto rho = insideVolVars.density(0);
        static const auto mu = insideVolVars.viscosity(0);
        static const auto rho_mu = rho/mu;
 
        // upwind term
        // evaluate the current wetting phase Darcy flux and resulting upwind weights
        using AdvectionType = GetPropType<TypeTag, Properties::AdvectionType>;
        static const Scalar upwindWeight = getParamFromGroup<Scalar>(problem.paramGroup(), "Flux.UpwindWeight");
        const auto flux = AdvectionType::flux(problem, element, fvGeometry, curElemVolVars, scvf, 0, elemFluxVarsCache);
        const auto insideWeight = std::signbit(flux) ? (1.0 - upwindWeight) : upwindWeight;
        const auto outsideWeight = 1.0 - insideWeight;
        const auto upwindTerm = rho*insideVolVars.mobility(0)*insideWeight + rho*outsideVolVars.mobility(0)*outsideWeight;
 
        // material law derivatives
        const auto insideSw = insideVolVars.saturation(0);
        const auto insidePc = insideVolVars.capillaryPressure();
        const auto dkrw_dsw_inside = insideFluidMatrixInteraction.dkrw_dsw(insideSw);
        const auto dsw_dpw_inside = -insideFluidMatrixInteraction.dsw_dpc(insidePc);
 
        // the transmissibility
        const auto tij = elemFluxVarsCache[scvf].advectionTij();
 
        // partial derivative of the wetting phase flux w.r.t. pw
        derivativeMatrices[insideScvIdx][conti0EqIdx][0] += tij*upwindTerm + rho_mu*flux*insideWeight*dkrw_dsw_inside*dsw_dpw_inside;
    }
 
    template<class PartialDerivativeMatrices>
    void addRobinFluxDerivatives(PartialDerivativeMatrices& derivativeMatrices,
                                 const Problem& problem,
                                 const Element& element,
                                 const FVElementGeometry& fvGeometry,
                                 const ElementVolumeVariables& curElemVolVars,
                                 const ElementFluxVariablesCache& elemFluxVarsCache,
                                 const SubControlVolumeFace& scvf) const
    {
        if constexpr(Detail::hasAddRobinFluxDerivatives<Problem,
            PartialDerivativeMatrices&, Element, FVElementGeometry,
            ElementVolumeVariables, ElementFluxVariablesCache, SubControlVolumeFace>()
        )
            problem.addRobinFluxDerivatives(derivativeMatrices, element, fvGeometry, curElemVolVars, elemFluxVarsCache, scvf);
    }
 
private:
    Implementation *asImp_()
    { return static_cast<Implementation *> (this); }
 
    const Implementation *asImp_() const
    { return static_cast<const Implementation *> (this); }
};
 
} // end namespace Dumux
 
#endif