porousmediumflow/nonequilibrium/localresidual.hh

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#ifndef DUMUX_NONEQUILIBRIUM_LOCAL_RESIDUAL_HH
#define DUMUX_NONEQUILIBRIUM_LOCAL_RESIDUAL_HH
 
#include <cmath>
#include <dumux/common/properties.hh>
#include <dumux/common/numeqvector.hh>
#include <dumux/porousmediumflow/nonequilibrium/thermal/localresidual.hh>
 
namespace Dumux {
 
// forward declaration
template<class TypeTag, bool enableChemicalNonEquilibrium>
class NonEquilibriumLocalResidualImplementation;
 
template <class TypeTag>
using NonEquilibriumLocalResidual = NonEquilibriumLocalResidualImplementation<TypeTag, GetPropType<TypeTag, Properties::ModelTraits>::enableChemicalNonEquilibrium()>;

template<class TypeTag>
class NonEquilibriumLocalResidualImplementation<TypeTag, false>: public GetPropType<TypeTag, Properties::EquilibriumLocalResidual>
{
    using ParentType = GetPropType<TypeTag, Properties::EquilibriumLocalResidual>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
    using NumEqVector = Dumux::NumEqVector<GetPropType<TypeTag, Properties::PrimaryVariables>>;
    using FVElementGeometry = typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView;
    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
    using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using EnergyLocalResidual = GetPropType<TypeTag, Properties::EnergyLocalResidual>;
    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
 
public:
    using ParentType::ParentType;

    NumEqVector computeSource(const Problem& problem,
                              const Element& element,
                              const FVElementGeometry& fvGeometry,
                              const ElementVolumeVariables& elemVolVars,
                              const SubControlVolume &scv) const
    {
        NumEqVector source(0.0);
 
        // add contributions from volume flux sources
        source += problem.source(element, fvGeometry, elemVolVars, scv);
 
        // add contribution from possible point sources
        source += problem.scvPointSources(element, fvGeometry, elemVolVars, scv);
 
        // Call the (kinetic) Energy module, for the source term.
        // it has to be called from here, because the mass transfered has to be known.
        if constexpr(ModelTraits::enableThermalNonEquilibrium())
        {
            EnergyLocalResidual::computeSourceEnergy(source,
                                                     element,
                                                     fvGeometry,
                                                     elemVolVars,
                                                     scv);
        }
 
        return source;
    }
 
};

template<class TypeTag>
class NonEquilibriumLocalResidualImplementation<TypeTag, true>: public GetPropType<TypeTag, Properties::EquilibriumLocalResidual>
{
    using ParentType = GetPropType<TypeTag, Properties::EquilibriumLocalResidual>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
    using FVElementGeometry = typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView;
    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
    using NumEqVector = Dumux::NumEqVector<GetPropType<TypeTag, Properties::PrimaryVariables>>;
    using FluxVariables = GetPropType<TypeTag, Properties::FluxVariables>;
    using ElementFluxVariablesCache = typename GetPropType<TypeTag, Properties::GridFluxVariablesCache>::LocalView;
    using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
    using EnergyLocalResidual = GetPropType<TypeTag, Properties::EnergyLocalResidual>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
 
    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
    using Indices = typename ModelTraits::Indices;
 
    static constexpr int numPhases = ModelTraits::numFluidPhases();
    static constexpr int numComponents = ModelTraits::numFluidComponents();
 
    static constexpr auto conti0EqIdx = Indices::conti0EqIdx;
    static constexpr auto comp0Idx = FluidSystem::comp0Idx;
    static constexpr auto phase0Idx = FluidSystem::phase0Idx;
    static constexpr auto phase1Idx = FluidSystem::phase1Idx;
 
    static_assert(numPhases > 1,
                  "chemical non-equlibrium only makes sense for multiple phases");
    static_assert(numPhases == numComponents,
                  "currently chemical non-equilibrium is only available when numPhases equals numComponents");
    static_assert(ModelTraits::useMoles(),
                  "chemical nonequilibrium can only be calculated based on mole fractions not mass fractions");
 
public:
     using ParentType::ParentType;
    NumEqVector computeStorage(const Problem& problem,
                               const SubControlVolume& scv,
                               const VolumeVariables& volVars) const
    {
       NumEqVector storage(0.0);
 
        // compute storage term of all components within all phases
        for (int phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx)
        {
            for (int compIdx = 0; compIdx < numComponents; ++compIdx)
            {
                 auto eqIdx = conti0EqIdx + phaseIdx*numComponents + compIdx;
                 storage[eqIdx] += volVars.porosity()
                                   * volVars.saturation(phaseIdx)
                                   * volVars.molarDensity(phaseIdx)
                                   * volVars.moleFraction(phaseIdx, compIdx);
            }
            EnergyLocalResidual::fluidPhaseStorage(storage, scv, volVars, phaseIdx);
        }
        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);
 
        // advective fluxes
        for (int phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx)
        {
            const auto diffusiveFluxes = fluxVars.molecularDiffusionFlux(phaseIdx);
            for (int compIdx = 0; compIdx < numComponents; ++compIdx)
            {
                // get equation index
                const auto eqIdx = conti0EqIdx + phaseIdx*numComponents + compIdx;
 
                // the physical quantities for which we perform upwinding
                const auto upwindTerm = [phaseIdx, compIdx] (const auto& volVars)
                { return volVars.molarDensity(phaseIdx)*volVars.moleFraction(phaseIdx, compIdx)*volVars.mobility(phaseIdx); };
 
                flux[eqIdx] += fluxVars.advectiveFlux(phaseIdx, upwindTerm);
 
                // do not add diffusive flux of main component, as that is not done in master as well
                if (compIdx == phaseIdx)
                        continue;
                //check for the reference system and adapt units of the diffusive flux accordingly.
                if (FluxVariables::MolecularDiffusionType::referenceSystemFormulation() == ReferenceSystemFormulation::massAveraged)
                    flux[eqIdx] += diffusiveFluxes[compIdx]/FluidSystem::molarMass(compIdx);
                else
                    flux[eqIdx] += diffusiveFluxes[compIdx];
            }
            EnergyLocalResidual::heatConvectionFlux(flux, fluxVars, phaseIdx);
        }

        EnergyLocalResidual::heatConductionFlux(flux, fluxVars);
 
        return flux;
    }

    NumEqVector computeSource(const Problem& problem,
                              const Element& element,
                              const FVElementGeometry& fvGeometry,
                              const ElementVolumeVariables& elemVolVars,
                              const SubControlVolume &scv) const
    {
        NumEqVector source(0.0);
        // In the case of a kinetic consideration, mass transfer
        // between phases is realized via source terms there is a
        // balance equation for each component in each phase
        const auto& volVars = elemVolVars[scv];
        std::array<std::array<Scalar, numComponents>, numPhases> componentIntoPhaseMassTransfer = {{{0.0},{0.0}}};
 
        //get characteristic length
        const Scalar characteristicLength   = volVars.characteristicLength()  ;
        const Scalar factorMassTransfer     = volVars.factorMassTransfer()  ;
 
        const Scalar awn = volVars.interfacialArea(phase0Idx, phase1Idx);
 
        for(int phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx)
        {
            const Scalar sherwoodNumber = volVars.sherwoodNumber(phaseIdx);
 
            for (int compIdx = 0; compIdx < numComponents; ++compIdx)
            {
                if (compIdx <= numPhases)
                {
                    //we only have to do the source calculation for one component going into the other phase as for each component: n_wn -> n_n = - n_n -> n_wn
                    if (phaseIdx == compIdx)
                        continue;
 
                    const Scalar xNonEquil = volVars.moleFraction(phaseIdx, compIdx);
 
                    //additionally get equilibrium values from volume variables
                    const Scalar xEquil = volVars.xEquil(phaseIdx, compIdx);
                    //get the diffusion coefficient
                    const Scalar diffCoeff = volVars.diffusionCoefficient(phaseIdx, FluidSystem::getMainComponent(phaseIdx), compIdx);
 
                    //now compute the flux
                    const Scalar compFluxIntoOtherPhase = factorMassTransfer * (xEquil-xNonEquil)/characteristicLength * awn * volVars.molarDensity(phaseIdx) * diffCoeff * sherwoodNumber;
 
                    componentIntoPhaseMassTransfer[phaseIdx][compIdx] += compFluxIntoOtherPhase;
                    componentIntoPhaseMassTransfer[compIdx][compIdx] -= compFluxIntoOtherPhase;
                }
            }
        }
 
        // Actually add the mass transfer to the sources which might
        // exist externally
        for (int phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx)
        {
            for (int compIdx = 0; compIdx < numComponents; ++compIdx)
            {
                const unsigned int eqIdx = conti0EqIdx + compIdx + phaseIdx*numComponents;
                source[eqIdx] += componentIntoPhaseMassTransfer[phaseIdx][compIdx];
 
                using std::isfinite;
                if (!isfinite(source[eqIdx]))
                    DUNE_THROW(NumericalProblem, "Calculated non-finite source");
            }
        }
 
        if constexpr (ModelTraits::enableThermalNonEquilibrium())
        {
            // Call the (kinetic) Energy module, for the source term.
            // it has to be called from here, because the mass transfered has to be known.
            EnergyLocalResidual::computeSourceEnergy(source,
                                                     element,
                                                     fvGeometry,
                                                     elemVolVars,
                                                     scv);
        }
 
        // add contributions from volume flux sources
        source += problem.source(element, fvGeometry, elemVolVars, scv);
 
        // add contribution from possible point sources
        source += problem.scvPointSources(element, fvGeometry, elemVolVars, scv);
 
        return source;
    }
 };
 
} // end namespace Dumux
 
#endif