freeflowporousmedium/couplingconditions.hh

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#ifndef DUMUX_MD_FREEFLOW_POROUSMEDIUM_COUPLINGCONDITIONS_HH
#define DUMUX_MD_FREEFLOW_POROUSMEDIUM_COUPLINGCONDITIONS_HH
 
#include <numeric>
 
#include <dune/common/exceptions.hh>
 
#include <dumux/common/properties.hh>
#include <dumux/common/math.hh>
 
#include <dumux/discretization/cellcentered/tpfa/computetransmissibility.hh>
 
#include <dumux/flux/darcyslaw_fwd.hh>
#include <dumux/flux/fickslaw_fwd.hh>
#include <dumux/flux/forchheimerslaw_fwd.hh>
 
#include <dumux/multidomain/boundary/freeflowporousmedium/traits.hh>
#include <dumux/multidomain/boundary/freeflowporousmedium/indexhelper.hh>
 
namespace Dumux {

struct FreeFlowPorousMediumCouplingOptions
{
    enum class DiffusionCoefficientAveragingType
    {
        harmonic, arithmethic, ffOnly, pmOnly
    };

    static DiffusionCoefficientAveragingType stringToEnum(DiffusionCoefficientAveragingType, const std::string& diffusionCoefficientAveragingType)
    {
        if (diffusionCoefficientAveragingType == "Harmonic")
            return DiffusionCoefficientAveragingType::harmonic;
        else if (diffusionCoefficientAveragingType == "Arithmethic")
            return DiffusionCoefficientAveragingType::arithmethic;
        else if (diffusionCoefficientAveragingType == "FreeFlowOnly")
            return DiffusionCoefficientAveragingType::ffOnly;
        else if (diffusionCoefficientAveragingType == "PorousMediumOnly")
            return DiffusionCoefficientAveragingType::pmOnly;
        else
            DUNE_THROW(Dune::IOError, "Unknown DiffusionCoefficientAveragingType");
    }
 
};
 
template<class MDTraits, class CouplingManager, bool enableEnergyBalance, bool isCompositional>
class FreeFlowPorousMediumCouplingConditionsImplementation;

template<class MDTraits, class CouplingManager>
using FreeFlowPorousMediumCouplingConditions
    = FreeFlowPorousMediumCouplingConditionsImplementation<
        MDTraits, CouplingManager,
        GetPropType<typename MDTraits::template SubDomain<0>::TypeTag, Properties::ModelTraits>::enableEnergyBalance(),
        (GetPropType<typename MDTraits::template SubDomain<0>::TypeTag, Properties::ModelTraits>::numFluidComponents() > 1)
    >;

template<class MDTraits, class CouplingManager>
class FreeFlowPorousMediumCouplingConditionsImplementationBase
{
    using Scalar = typename MDTraits::Scalar;
 
    template<std::size_t id> using SubDomainTypeTag = typename MDTraits::template SubDomain<id>::TypeTag;
    template<std::size_t id> using GridGeometry = GetPropType<SubDomainTypeTag<id>, Properties::GridGeometry>;
    template<std::size_t id> using Element = typename GridGeometry<id>::GridView::template Codim<0>::Entity;
    template<std::size_t id> using FVElementGeometry = typename GridGeometry<id>::LocalView;
    template<std::size_t id> using SubControlVolumeFace = typename GridGeometry<id>::LocalView::SubControlVolumeFace;
    template<std::size_t id> using SubControlVolume = typename GridGeometry<id>::LocalView::SubControlVolume;
    template<std::size_t id> using Indices = typename GetPropType<SubDomainTypeTag<id>, Properties::ModelTraits>::Indices;
    template<std::size_t id> using ElementVolumeVariables = typename GetPropType<SubDomainTypeTag<id>, Properties::GridVolumeVariables>::LocalView;
    template<std::size_t id> using VolumeVariables = typename GetPropType<SubDomainTypeTag<id>, Properties::GridVolumeVariables>::VolumeVariables;
    template<std::size_t id> using Problem = GetPropType<SubDomainTypeTag<id>, Properties::Problem>;
    template<std::size_t id> using FluidSystem = GetPropType<SubDomainTypeTag<id>, Properties::FluidSystem>;
    template<std::size_t id> using ModelTraits = GetPropType<SubDomainTypeTag<id>, Properties::ModelTraits>;
    template<std::size_t id> using GlobalPosition = typename Element<id>::Geometry::GlobalCoordinate;
    template<std::size_t id> using NumEqVector = typename Problem<id>::Traits::NumEqVector;
 
public:
    static constexpr auto freeFlowMomentumIndex = CouplingManager::freeFlowMomentumIndex;
    static constexpr auto freeFlowMassIndex = CouplingManager::freeFlowMassIndex;
    static constexpr auto porousMediumIndex = CouplingManager::porousMediumIndex;
private:
 
    using AdvectionType = GetPropType<SubDomainTypeTag<porousMediumIndex>, Properties::AdvectionType>;
    using DarcysLaw = Dumux::DarcysLaw<SubDomainTypeTag<porousMediumIndex>>;
    using ForchheimersLaw = Dumux::ForchheimersLaw<SubDomainTypeTag<porousMediumIndex>>;
 
    static constexpr bool adapterUsed = ModelTraits<porousMediumIndex>::numFluidPhases() > 1;
    using IndexHelper = FreeFlowPorousMediumCoupling::IndexHelper<freeFlowMassIndex, porousMediumIndex, FluidSystem<freeFlowMassIndex>, adapterUsed>;
 
    static constexpr int enableEnergyBalance = GetPropType<SubDomainTypeTag<freeFlowMassIndex>, Properties::ModelTraits>::enableEnergyBalance();
    static_assert(GetPropType<SubDomainTypeTag<porousMediumIndex>, Properties::ModelTraits>::enableEnergyBalance() == enableEnergyBalance,
                  "All submodels must both be either isothermal or non-isothermal");
 
    static_assert(FreeFlowPorousMediumCoupling::IsSameFluidSystem<FluidSystem<freeFlowMassIndex>,
                  FluidSystem<porousMediumIndex>>::value,
                  "All submodels must use the same fluid system");
 
    using DiffusionCoefficientAveragingType = typename FreeFlowPorousMediumCouplingOptions::DiffusionCoefficientAveragingType;
 
public:
    template<std::size_t i>
    static constexpr auto couplingPhaseIdx(Dune::index_constant<i> id, int coupledPhaseIdx = 0)
    { return IndexHelper::couplingPhaseIdx(id, coupledPhaseIdx); }

    template<std::size_t i>
    static constexpr auto couplingCompIdx(Dune::index_constant<i> id, int coupledCompIdx)
    { return IndexHelper::couplingCompIdx(id, coupledCompIdx); }

    template<class Context>
    static auto darcyPermeability(const FVElementGeometry<freeFlowMomentumIndex>& fvGeometry,
                                  const SubControlVolumeFace<freeFlowMomentumIndex>& scvf,
                                  const Context& context)
    { return context.volVars.permeability(); }

    template<class Context>
    static NumEqVector<freeFlowMomentumIndex> momentumCouplingCondition(const FVElementGeometry<freeFlowMomentumIndex>& fvGeometry,
                                                                        const SubControlVolumeFace<freeFlowMomentumIndex>& scvf,
                                                                        const ElementVolumeVariables<freeFlowMomentumIndex>& elemVolVars,
                                                                        const Context& context)
    {
        static constexpr auto numPhasesDarcy = GetPropType<SubDomainTypeTag<porousMediumIndex>, Properties::ModelTraits>::numFluidPhases();
        NumEqVector<freeFlowMomentumIndex> momentumFlux(0.0);
 
        if (!scvf.isFrontal())
            return momentumFlux;
 
        const auto pmPhaseIdx = couplingPhaseIdx(porousMediumIndex);
 
        if(numPhasesDarcy > 1)
            momentumFlux[scvf.normalAxis()] = context.volVars.pressure(pmPhaseIdx);
        else // use pressure reconstruction for single phase models
            momentumFlux[scvf.normalAxis()] = pressureAtInterface_(fvGeometry, scvf, elemVolVars, context);
 
        // TODO: generalize for permeability tensors
 
        // normalize pressure
        momentumFlux[scvf.normalAxis()] -= elemVolVars.gridVolVars().problem().referencePressure(fvGeometry.element(), fvGeometry, scvf);
 
        momentumFlux[scvf.normalAxis()] *= scvf.directionSign();
 
        return momentumFlux;
    }

     */
    static Scalar advectiveFlux(const Scalar insideQuantity, const Scalar outsideQuantity, const Scalar volumeFlow, bool insideIsUpstream)
    {
        const Scalar upwindWeight = 1.0; //TODO use Flux.UpwindWeight or something like Coupling.UpwindWeight?
 
        if(insideIsUpstream)
            return (upwindWeight * insideQuantity + (1.0 - upwindWeight) * outsideQuantity) * volumeFlow;
        else
            return (upwindWeight * outsideQuantity + (1.0 - upwindWeight) * insideQuantity) * volumeFlow;
    }
 
protected:

    template<std::size_t i, std::size_t j>
    Scalar transmissibility_(Dune::index_constant<i> domainI,
                             Dune::index_constant<j> domainJ,
                             const Scalar insideDistance,
                             const Scalar outsideDistance,
                             const Scalar avgQuantityI,
                             const Scalar avgQuantityJ,
                             const DiffusionCoefficientAveragingType diffCoeffAvgType) const
    {
        const Scalar totalDistance = insideDistance + outsideDistance;
        if(diffCoeffAvgType == DiffusionCoefficientAveragingType::harmonic)
        {
            return harmonicMean(avgQuantityI, avgQuantityJ, insideDistance, outsideDistance)
                   / totalDistance;
        }
        else if(diffCoeffAvgType == DiffusionCoefficientAveragingType::arithmethic)
        {
            return arithmeticMean(avgQuantityI, avgQuantityJ, insideDistance, outsideDistance)
                   / totalDistance;
        }
        else if(diffCoeffAvgType == DiffusionCoefficientAveragingType::ffOnly)
            return domainI == freeFlowMassIndex
                            ? avgQuantityI / totalDistance
                            : avgQuantityJ / totalDistance;
 
        else // diffCoeffAvgType == DiffusionCoefficientAveragingType::pmOnly)
            return domainI == porousMediumIndex
                            ? avgQuantityI / totalDistance
                            : avgQuantityJ / totalDistance;
    }

    template<class Scv, class Scvf>
    Scalar getDistance_(const Scv& scv, const Scvf& scvf) const
    {
        return (scv.dofPosition() - scvf.ipGlobal()).two_norm();
    }

    template<std::size_t i, std::size_t j, bool isNI = enableEnergyBalance, typename std::enable_if_t<isNI, int> = 0>
    Scalar conductiveEnergyFlux_(Dune::index_constant<i> domainI,
                                 Dune::index_constant<j> domainJ,
                                 const FVElementGeometry<i>& fvGeometryI,
                                 const FVElementGeometry<j>& fvGeometryJ,
                                 const SubControlVolumeFace<i>& scvfI,
                                 const SubControlVolume<i>& scvI,
                                 const SubControlVolume<j>& scvJ,
                                 const VolumeVariables<i>& volVarsI,
                                 const VolumeVariables<j>& volVarsJ,
                                 const DiffusionCoefficientAveragingType diffCoeffAvgType) const
    {
        const Scalar insideDistance = getDistance_(scvI, scvfI);
        const Scalar outsideDistance = getDistance_(scvJ, scvfI);
 
        const Scalar deltaT = volVarsJ.temperature() - volVarsI.temperature();
        const Scalar tij = transmissibility_(
            domainI, domainJ,
            insideDistance, outsideDistance,
            volVarsI.effectiveThermalConductivity(), volVarsJ.effectiveThermalConductivity(),
            diffCoeffAvgType
        );
 
        return -tij * deltaT;
    }

    template<class CouplingContext>
    static Scalar pressureAtInterface_(const FVElementGeometry<freeFlowMomentumIndex>& fvGeometry,
                                       const SubControlVolumeFace<freeFlowMomentumIndex>& scvf,
                                       const ElementVolumeVariables<freeFlowMomentumIndex>& elemVolVars,
                                       const CouplingContext& context)
    {
        GlobalPosition<freeFlowMomentumIndex> velocity(0.0);
        const auto& scv = fvGeometry.scv(scvf.insideScvIdx());
        velocity[scv.dofAxis()] = elemVolVars[scv].velocity();
        const auto& pmScvf = context.fvGeometry.scvf(context.porousMediumScvfIdx);
        return computeCouplingPhasePressureAtInterface_(context.fvGeometry, pmScvf, context.volVars, context.gravity, velocity, AdvectionType());
    }

     */
    static Scalar computeCouplingPhasePressureAtInterface_(const FVElementGeometry<porousMediumIndex>& fvGeometry,
                                                           const SubControlVolumeFace<porousMediumIndex>& scvf,
                                                           const VolumeVariables<porousMediumIndex>& volVars,
                                                           const typename Element<freeFlowMomentumIndex>::Geometry::GlobalCoordinate& couplingPhaseVelocity,
                                                           ForchheimersLaw)
    {
        DUNE_THROW(Dune::NotImplemented, "Forchheimer's law pressure reconstruction");
    }

     */
    static Scalar computeCouplingPhasePressureAtInterface_(const FVElementGeometry<porousMediumIndex>& fvGeometry,
                                                           const SubControlVolumeFace<porousMediumIndex>& scvf,
                                                           const VolumeVariables<porousMediumIndex>& volVars,
                                                           const typename Element<freeFlowMomentumIndex>::Geometry::GlobalCoordinate& gravity,
                                                           const typename Element<freeFlowMomentumIndex>::Geometry::GlobalCoordinate& couplingPhaseVelocity,
                                                           DarcysLaw)
    {
        const auto pmPhaseIdx = couplingPhaseIdx(porousMediumIndex);
        const Scalar couplingPhaseCellCenterPressure = volVars.pressure(pmPhaseIdx);
        const Scalar couplingPhaseMobility = volVars.mobility(pmPhaseIdx);
        const Scalar couplingPhaseDensity = volVars.density(pmPhaseIdx);
        const auto K = volVars.permeability();
 
        // A tpfa approximation yields (works if mobility != 0)
        // v*n = -kr/mu*K * (gradP - rho*g)*n = mobility*(ti*(p_center - p_interface) + rho*n^TKg)
        // -> p_interface = (1/mobility * (-v*n) + rho*n^TKg)/ti + p_center
        // where v is the free-flow velocity (couplingPhaseVelocity)
        const auto alpha = vtmv(scvf.unitOuterNormal(), K, gravity);
 
        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
        const auto ti = computeTpfaTransmissibility(scvf, insideScv, K, 1.0);
 
        return (-1/couplingPhaseMobility * (scvf.unitOuterNormal() * couplingPhaseVelocity) + couplingPhaseDensity * alpha)/ti
               + couplingPhaseCellCenterPressure;
    }
};

template<class MDTraits, class CouplingManager, bool enableEnergyBalance>
class FreeFlowPorousMediumCouplingConditionsImplementation<MDTraits, CouplingManager, enableEnergyBalance, false>
: public FreeFlowPorousMediumCouplingConditionsImplementationBase<MDTraits, CouplingManager>
{
    using ParentType = FreeFlowPorousMediumCouplingConditionsImplementationBase<MDTraits, CouplingManager>;
    using Scalar = typename MDTraits::Scalar;
 
    // the sub domain type tags
    template<std::size_t id>
    using SubDomainTypeTag = typename MDTraits::template SubDomain<id>::TypeTag;
 
    template<std::size_t id> using GridGeometry = GetPropType<SubDomainTypeTag<id>, Properties::GridGeometry>;
    template<std::size_t id> using Element = typename GridGeometry<id>::GridView::template Codim<0>::Entity;
    template<std::size_t id> using FVElementGeometry = typename GridGeometry<id>::LocalView;
    template<std::size_t id> using SubControlVolumeFace = typename GridGeometry<id>::LocalView::SubControlVolumeFace;
    template<std::size_t id> using SubControlVolume = typename GridGeometry<id>::LocalView::SubControlVolume;
    template<std::size_t id> using Indices = typename GetPropType<SubDomainTypeTag<id>, Properties::ModelTraits>::Indices;
    template<std::size_t id> using ElementVolumeVariables = typename GetPropType<SubDomainTypeTag<id>, Properties::GridVolumeVariables>::LocalView;
    template<std::size_t id> using VolumeVariables  = typename GetPropType<SubDomainTypeTag<id>, Properties::GridVolumeVariables>::VolumeVariables;
 
    static_assert(GetPropType<SubDomainTypeTag<ParentType::porousMediumIndex>, Properties::ModelTraits>::numFluidComponents() == GetPropType<SubDomainTypeTag<ParentType::porousMediumIndex>, Properties::ModelTraits>::numFluidPhases(),
                  "Darcy Model must not be compositional");
 
    using DiffusionCoefficientAveragingType = typename FreeFlowPorousMediumCouplingOptions::DiffusionCoefficientAveragingType;
 
public:
    using ParentType::ParentType;
    using ParentType::couplingPhaseIdx;

    template<std::size_t i, std::size_t j, class CouplingContext>
    static Scalar massCouplingCondition(Dune::index_constant<i> domainI,
                                        Dune::index_constant<j> domainJ,
                                        const FVElementGeometry<i>& fvGeometry,
                                        const SubControlVolumeFace<i>& scvf,
                                        const ElementVolumeVariables<i>& insideVolVars,
                                        const CouplingContext& context)
    {
        const Scalar normalVelocity = context.velocity * scvf.unitOuterNormal();
        const Scalar darcyDensity = insideVolVars[scvf.insideScvIdx()].density(couplingPhaseIdx(ParentType::porousMediumIndex));
        const Scalar stokesDensity = context.volVars.density();
        const bool insideIsUpstream = normalVelocity > 0.0;
        return ParentType::advectiveFlux(darcyDensity, stokesDensity, normalVelocity, insideIsUpstream);
    }

    template<bool isNI = enableEnergyBalance, typename std::enable_if_t<isNI, int> = 0>
    Scalar energyCouplingCondition(const Element<ParentType::porousMediumIndex>& element,
                                   const FVElementGeometry<ParentType::porousMediumIndex>& fvGeometry,
                                   const ElementVolumeVariables<ParentType::porousMediumIndex>& darcyElemVolVars,
                                   const SubControlVolumeFace<ParentType::porousMediumIndex>& scvf,
                                   const DiffusionCoefficientAveragingType diffCoeffAvgType = DiffusionCoefficientAveragingType::ffOnly) const
    {
        DUNE_THROW(Dune::NotImplemented, "Energy coupling condition");
    }

    template<bool isNI = enableEnergyBalance, typename std::enable_if_t<isNI, int> = 0>
    Scalar energyCouplingCondition(const Element<ParentType::freeFlowMassIndex>& element,
                                   const FVElementGeometry<ParentType::freeFlowMassIndex>& fvGeometry,
                                   const ElementVolumeVariables<ParentType::freeFlowMassIndex>& stokesElemVolVars,
                                   const SubControlVolumeFace<ParentType::freeFlowMassIndex>& scvf,
                                   const DiffusionCoefficientAveragingType diffCoeffAvgType = DiffusionCoefficientAveragingType::ffOnly) const
    {
        DUNE_THROW(Dune::NotImplemented, "Energy coupling condition");
    }
 
private:
 
 

    template<std::size_t i, std::size_t j, bool isNI = enableEnergyBalance, typename std::enable_if_t<isNI, int> = 0>
    Scalar energyFlux_(Dune::index_constant<i> domainI,
                       Dune::index_constant<j> domainJ,
                       const FVElementGeometry<i>& insideFvGeometry,
                       const FVElementGeometry<j>& outsideFvGeometry,
                       const SubControlVolumeFace<i>& scvf,
                       const VolumeVariables<i>& insideVolVars,
                       const VolumeVariables<j>& outsideVolVars,
                       const Scalar velocity,
                       const bool insideIsUpstream,
                       const DiffusionCoefficientAveragingType diffCoeffAvgType) const
    {
        Scalar flux(0.0);
 
        const auto& insideScv = (*scvs(insideFvGeometry).begin());
        const auto& outsideScv = (*scvs(outsideFvGeometry).begin());
 
        // convective fluxes
        const Scalar insideTerm = insideVolVars.density(couplingPhaseIdx(domainI)) * insideVolVars.enthalpy(couplingPhaseIdx(domainI));
        const Scalar outsideTerm = outsideVolVars.density(couplingPhaseIdx(domainJ)) * outsideVolVars.enthalpy(couplingPhaseIdx(domainJ));
 
        flux += this->advectiveFlux(insideTerm, outsideTerm, velocity, insideIsUpstream);
 
        flux += this->conductiveEnergyFlux_(domainI, domainJ, insideFvGeometry, outsideFvGeometry, scvf, insideScv, outsideScv, insideVolVars, outsideVolVars, diffCoeffAvgType);
 
        return flux;
    }
 
};
 
} // end namespace Dumux
 
#endif