fv3dtransportadaptive.hh

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#ifndef DUMUX_FV3DTRANSPORT2P2C_ADAPTIVE_HH
#define DUMUX_FV3DTRANSPORT2P2C_ADAPTIVE_HH
 
#include <dune/grid/common/gridenums.hh>
#include <dune/common/float_cmp.hh>
 
#include <dumux/common/math.hh>
#include <dumux/linear/vectorexchange.hh>
 
#include "adaptiveproperties.hh"
#include "fvtransport.hh"
 
namespace Dumux {
template<class TypeTag>
class FV3dTransport2P2CAdaptive : public FVTransport2P2C<TypeTag>
{
    using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
 
    using SpatialParams = GetPropType<TypeTag, Properties::SpatialParams>;
    using MaterialLaw = typename SpatialParams::MaterialLaw;
 
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
    using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
 
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using FluidState = GetPropType<TypeTag, Properties::FluidState>;
 
    using CellData = GetPropType<TypeTag, Properties::CellData>;
 
    using TransportSolutionType = GetPropType<TypeTag, Properties::TransportSolutionType>;
 
    enum
    {
        dim = GridView::dimension, dimWorld = GridView::dimensionworld,
        NumPhases = getPropValue<TypeTag, Properties::NumPhases>()
    };
    enum
    {
        pw = Indices::pressureW,
        pn = Indices::pressureN,
        Sw = Indices::saturationW,
        Sn = Indices::saturationN
    };
    enum
    {
        wPhaseIdx = Indices::wPhaseIdx, nPhaseIdx = Indices::nPhaseIdx,
        wCompIdx = Indices::wPhaseIdx, nCompIdx = Indices::nPhaseIdx,
        contiWEqIdx=Indices::contiWEqIdx, contiNEqIdx=Indices::contiNEqIdx
    };
 
    using Element = typename GridView::Traits::template Codim<0>::Entity;
    using Grid = typename GridView::Grid;
    using Intersection = typename GridView::Intersection;
    using IntersectionIterator = typename GridView::IntersectionIterator;
 
    using TransmissivityMatrix = Dune::FieldVector<Scalar,dim+1>;
    using GlobalPosition = Dune::FieldVector<Scalar, dimWorld>;
    using DimMatrix = Dune::FieldMatrix<Scalar, dim, dim>;
    using PhaseVector = Dune::FieldVector<Scalar, NumPhases>;
    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;

    Problem& problem()
    { return problem_; }
 
public:
    virtual void update(const Scalar t, Scalar& dt, TransportSolutionType& updateVec,
                        bool impes = false);
 
    void getMpfaFlux(Dune::FieldVector<Scalar, 2>&, Dune::FieldVector<Scalar, 2>&,
            const IntersectionIterator&, CellData&);

    FV3dTransport2P2CAdaptive(Problem& problem) : FVTransport2P2C<TypeTag>(problem),
        problem_(problem), enableMPFA(false)
    {
        enableMPFA = getParam<bool>("GridAdapt.EnableMultiPointFluxApproximation");
    }
 
    virtual ~FV3dTransport2P2CAdaptive()
    {
    }
 
protected:
    Problem& problem_;
 
    bool enableMPFA; 

    static const int pressureType = getPropValue<TypeTag, Properties::PressureFormulation>();
};

template<class TypeTag>
void FV3dTransport2P2CAdaptive<TypeTag>::update(const Scalar t, Scalar& dt,
                              TransportSolutionType& updateVec, bool impet)
{
    this->impet_ = impet;
 
    // initialize dt very large
    dt = 1E100;
    this->averagedFaces_ = 0;
 
    // resize update vector and set to zero
    int size_ = problem_.gridView().size(0);
    updateVec.resize(getPropValue<TypeTag, Properties::NumComponents>());
    updateVec[wCompIdx].resize(size_);
    updateVec[nCompIdx].resize(size_);
    updateVec[wCompIdx] = 0;
    updateVec[nCompIdx] = 0;
    //also resize PV vector if necessary
    if(this->totalConcentration_.size() != size_)
    {
        this->totalConcentration_[wCompIdx].resize(size_);
        this->totalConcentration_[nCompIdx].resize(size_);
        // copy data //TODO: remove this, remove PM Transport Vector!!
        // loop thorugh all elements
        for (int i = 0; i< problem().gridView().size(0); i++)
        {
            CellData& cellDataI = problem().variables().cellData(i);
            for(int compIdx = 0; compIdx < getPropValue<TypeTag, Properties::NumComponents>(); compIdx++)
            {
                this->totalConcentration_[compIdx][i]
                        = cellDataI.totalConcentration(compIdx);
            }
        }
    }
    if (this->localTimeStepping_)
    {
        if (this->timeStepData_.size() != size_)
            this->timeStepData_.resize(size_);
    }
 
    // Cell which restricts time step size
    int restrictingCell = -1;
 
    Dune::FieldVector<Scalar, 2> entries(0.), timestepFlux(0.);
    // compute update vector
    for (const auto& element : elements(problem().gridView()))
    {
        // get cell infos
        int globalIdxI = problem().variables().index(element);
        CellData& cellDataI = problem().variables().cellData(globalIdxI);
 
        if(!impet && cellDataI.subdomain()!=2)   // estimate only necessary in subdomain
            continue;
 
        // some variables for time step calculation
        double sumfactorin = 0;
        double sumfactorout = 0;
 
        // run through all intersections with neighbors and boundary
        const auto isEndIt = problem().gridView().iend(element);
        for (auto isIt = problem().gridView().ibegin(element); isIt != isEndIt; ++isIt)
        {
            const auto& intersection = *isIt;
 
            // handle interior face
            if (intersection.neighbor())
            {
                if (enableMPFA && intersection.outside().level() != element.level())
                    getMpfaFlux(entries, timestepFlux, isIt, cellDataI);
                else
                    this->getFlux(entries, timestepFlux, intersection, cellDataI);
            }
 
            //     Boundary Face
            if (intersection.boundary())
            {
                this->getFluxOnBoundary(entries, timestepFlux, intersection, cellDataI);
            }
 
            if (this->localTimeStepping_)
            {
                int indexInInside = intersection.indexInInside();
                typename FVTransport2P2C<TypeTag>::LocalTimesteppingData& localData = this->timeStepData_[globalIdxI];
                if (localData.faceTargetDt[indexInInside] < this->accumulatedDt_ + this->dtThreshold_)
                {
                    localData.faceFluxes[indexInInside] = entries;
                }
            }
            else
            {
            // add to update vector
                updateVec[wCompIdx][globalIdxI] += entries[wCompIdx];
                updateVec[nCompIdx][globalIdxI] += entries[nCompIdx];
            }
            // for time step calculation
            sumfactorin += timestepFlux[0];
            sumfactorout += timestepFlux[1];
 
        }// end all intersections
 
        if (this->localTimeStepping_)
        {
            typename FVTransport2P2C<TypeTag>::LocalTimesteppingData& localData = this->timeStepData_[globalIdxI];
            for (int i=0; i < 2*dim; i++)
            {
                updateVec[wCompIdx][globalIdxI] += localData.faceFluxes[i][wCompIdx];
                updateVec[nCompIdx][globalIdxI] += localData.faceFluxes[i][nCompIdx];
            }
        }
 
        /***********     Handle source term     ***************/
        PrimaryVariables q(NAN);
        problem().source(q, element);
        updateVec[wCompIdx][globalIdxI] += q[contiWEqIdx];
        updateVec[nCompIdx][globalIdxI] += q[contiNEqIdx];
 
        // account for porosity
        using std::max;
        sumfactorin = max(sumfactorin,sumfactorout)
                        / problem().spatialParams().porosity(element);
 
        //calculate time step
        if (this->localTimeStepping_)
        {
            this->timeStepData_[globalIdxI].dt = 1./sumfactorin;
            if ( 1./sumfactorin < dt)
            {
                dt = 1./sumfactorin;
                restrictingCell= globalIdxI;
            }
        }
        else
        {
            if ( 1./sumfactorin < dt)
            {
                dt = 1./sumfactorin;
                restrictingCell= globalIdxI;
            }
        }
    } // end grid traversal
 
#if HAVE_MPI
    // communicate updated values
    using SolutionTypes = GetProp<TypeTag, Properties::SolutionTypes>;
    using ElementMapper = typename SolutionTypes::ElementMapper;
    using DataHandle = VectorExchange<ElementMapper, Dune::BlockVector<Dune::FieldVector<Scalar, 1> > >;
    for (int i = 0; i < updateVec.size(); i++)
    {
        DataHandle dataHandle(problem().variables().elementMapper(), updateVec[i]);
        problem_.gridView().template communicate<DataHandle>(dataHandle,
                                                            Dune::InteriorBorder_All_Interface,
                                                            Dune::ForwardCommunication);
    }
    dt = problem().gridView().comm().min(dt);
#endif
 
    if(impet)
    {
        Dune::dinfo << "Timestep restricted by CellIdx " << restrictingCell << " leads to dt = "
                <<dt * getParam<Scalar>("Impet.CFLFactor")<< std::endl;
        if(this->averagedFaces_ != 0)
            Dune::dwarn  << " Averageing done for " << this->averagedFaces_ << " faces. "<< std::endl;
    }
    return;
}

template<class TypeTag>
void FV3dTransport2P2CAdaptive<TypeTag>::getMpfaFlux(Dune::FieldVector<Scalar, 2>& fluxEntries,
                              Dune::FieldVector<Scalar, 2>& timestepFlux,
                              const IntersectionIterator& isIt, CellData& cellDataI)
{
    const auto& intersection = *isIt;
 
    fluxEntries = 0.;
    timestepFlux = 0.;
    // cell information
    auto elementI = intersection.inside();
    int globalIdxI = problem().variables().index(elementI);
 
    // get position
    const GlobalPosition globalPos = elementI.geometry().center();
    const GlobalPosition& gravity_ = problem().gravity();
    // cell volume, assume linear map here
    Scalar volume = elementI.geometry().volume();
 
    // get values of cell I
    Scalar pressI = problem().pressureModel().pressure(globalIdxI);
    Scalar pcI = cellDataI.capillaryPressure();
 
    PhaseVector SmobI(0.);
    using std::max;
    SmobI[wPhaseIdx] = max((cellDataI.saturation(wPhaseIdx)
                            - problem().spatialParams().materialLawParams(elementI).swr())
                            , 1e-2);
    SmobI[nPhaseIdx] = max((cellDataI.saturation(nPhaseIdx)
                                - problem().spatialParams().materialLawParams(elementI).snr())
                            , 1e-2);
 
    Scalar densityWI (0.), densityNWI(0.);
    densityWI= cellDataI.density(wPhaseIdx);
    densityNWI = cellDataI.density(nPhaseIdx);
 
    PhaseVector potential(0.);
 
    // access neighbor
    auto neighbor = intersection.outside();
    int globalIdxJ = problem().variables().index(neighbor);
    CellData& cellDataJ = problem().variables().cellData(globalIdxJ);
 
    // neighbor cell center in global coordinates
    const GlobalPosition& globalPosNeighbor = neighbor.geometry().center();
 
    // distance vector between barycenters
    GlobalPosition distVec = globalPosNeighbor - globalPos;
    // compute distance between cell centers
    Scalar dist = distVec.two_norm();
 
    GlobalPosition unitDistVec(distVec);
    unitDistVec /= dist;
 
    // phase densities in neighbor
    Scalar densityWJ (0.), densityNWJ(0.);
    densityWJ = cellDataJ.density(wPhaseIdx);
    densityNWJ = cellDataJ.density(nPhaseIdx);
 
    // average phase densities with central weighting
    double densityW_mean = (densityWI + densityWJ) * 0.5;
    double densityNW_mean = (densityNWI + densityNWJ) * 0.5;
 
    double pressJ = problem().pressureModel().pressure(globalIdxJ);
    Scalar pcJ = cellDataJ.capillaryPressure();
 
    // determine potentials for upwind
    GlobalPosition globalPos3(0.);
    int globalIdx3=-1;
    GlobalPosition globalPos4(0.);
    int globalIdx4=-1;
    TransmissivityMatrix T(0.);
    TransmissivityMatrix additionalT(0.);
    // prepare second interaction region
    GlobalPosition globalPosAdditional3(0.);
    int globalIdxAdditional3=-1;
    GlobalPosition globalPosAdditional4(0.);
    int globalIdxAdditional4=-1;
 
    int halfedgesStored
        = problem().variables().getMpfaData3D(intersection, T, globalPos3, globalIdx3, globalPos4, globalIdx4  );
    if (halfedgesStored == 0)
        halfedgesStored = problem().pressureModel().computeTransmissibilities(isIt,T,
                globalPos3, globalIdx3,  globalPos4, globalIdx4  );
 
    // acess cell 3&4 and prepare mpfa
    Scalar press3 = problem().pressureModel().pressure(globalIdx3);
    CellData& cellData3 = problem().variables().cellData(globalIdx3);
    Scalar pc3 = cellData3.capillaryPressure();
    Scalar press4 = problem().pressureModel().pressure(globalIdx4);
    CellData& cellData4 = problem().variables().cellData(globalIdx4);
    Scalar pc4 = cellData4.capillaryPressure();
    Scalar temp1 = globalPos * gravity_;
    Scalar temp2 = globalPosNeighbor * gravity_;
    Scalar temp3 = globalPos3 * gravity_;
    Scalar temp4 = globalPos4 * gravity_;
    if(pressureType==pw)
    {
        potential[wPhaseIdx] += (pressI-temp1*densityW_mean) * T[0]
                        +(pressJ-temp2*densityW_mean) * T[1]
                        +(press3- temp3*densityW_mean) * T[2]
                        +(press4- temp4*densityW_mean) * T[3];
        potential[nPhaseIdx] += (pressI+pcI-temp1*densityNW_mean) * T[0]
                        +(pressJ+pcJ-temp2*densityNW_mean) * T[1]
                        +(press3+pc3- temp3*densityNW_mean) * T[2]
                        +(press4+pc4- temp4*densityNW_mean) * T[3];
    }
    else if(pressureType==pn)
    {
        potential[wPhaseIdx] += (pressI-pcI-temp1*densityW_mean) * T[0]
                      + (pressJ-pcJ-temp2*densityW_mean) * T[1]
                      + (press3-pc3- temp3*densityW_mean) * T[2]
                      + (press4-pc4- temp4*densityW_mean) * T[3];
        potential[nPhaseIdx] += (pressI-temp1*densityNW_mean) * T[0]
                      + (pressJ-temp2*densityNW_mean) * T[1]
                      + (press3-temp3*densityNW_mean) * T[2]
                      + (press4-temp4*densityNW_mean) * T[3];
    }
    // regard more interaction regions, if there are more
    if(halfedgesStored != 1)
    {
        for(int banana = 1; banana < halfedgesStored; banana ++)
        {
            // get data for second interaction region
            problem().variables().getMpfaData3D(intersection, additionalT,
                            globalPosAdditional3, globalIdxAdditional3,
                            globalPosAdditional4, globalIdxAdditional4 ,
                            banana); // offset for second interaction region
 
            Scalar gravityContributionAdditonal
                = temp1 * additionalT[0] + temp2 * additionalT[1]
                    + globalPosAdditional3*gravity_ * additionalT[2]
                    + globalPosAdditional4*gravity_ * additionalT[3];
            CellData& cellDataA3 = problem().variables().cellData(globalIdxAdditional3);
            CellData& cellDataA4 = problem().variables().cellData(globalIdxAdditional4);
 
            if(pressureType==pw)
            {
                potential[wPhaseIdx] += pressI * additionalT[0] + pressJ * additionalT[1]
                    +problem().pressureModel().pressure(globalIdxAdditional3) * additionalT[2]
                    +problem().pressureModel().pressure(globalIdxAdditional4)* additionalT[3];
                potential[nPhaseIdx] += (pressI+pcI) * additionalT[0] + (pressJ+pcJ) * additionalT[1]
                    +(problem().pressureModel().pressure(globalIdxAdditional3)+cellDataA3.capillaryPressure()) * additionalT[2]
                    +(problem().pressureModel().pressure(globalIdxAdditional4)+cellDataA4.capillaryPressure()) * additionalT[3];
            }
            else if(pressureType==pn)
            {
                potential[wPhaseIdx] += (pressI-pcI) * additionalT[0] + (pressJ-pcJ) * additionalT[1]
                  + (problem().pressureModel().pressure(globalIdxAdditional3)-cellDataA3.capillaryPressure()) * additionalT[2]
                  + (problem().pressureModel().pressure(globalIdxAdditional4)-cellDataA4.capillaryPressure()) * additionalT[3];
                potential[nPhaseIdx] += pressI * additionalT[0] + pressJ * additionalT[1]
                  + problem().pressureModel().pressure(globalIdxAdditional3) * additionalT[2]
                  + problem().pressureModel().pressure(globalIdxAdditional4) * additionalT[3];
            }
            potential[wPhaseIdx] -= gravityContributionAdditonal * densityW_mean;
            potential[nPhaseIdx] -= gravityContributionAdditonal * densityNW_mean;
        }
    }   //end of mpfa specific stuff
 
    // determine upwinding direction, perform upwinding if possible
    Dune::FieldVector<bool, NumPhases> doUpwinding(true);
    PhaseVector lambda(0.);
    for(int phaseIdx = 0; phaseIdx < NumPhases; phaseIdx++)
    {
        int contiEqIdx = 0;
        if(phaseIdx == wPhaseIdx)
            contiEqIdx = contiWEqIdx;
        else
            contiEqIdx = contiNEqIdx;
 
        if(!this->impet_ or !this->restrictFluxInTransport_) // perform a strict uwpind scheme
        {
            if(potential[phaseIdx] > 0.)
            {
                lambda[phaseIdx] = cellDataI.mobility(phaseIdx);
                cellDataI.setUpwindCell(intersection.indexInInside(), contiEqIdx, true);
            }
            else if(potential[phaseIdx] < 0.)
            {
                lambda[phaseIdx] = cellDataJ.mobility(phaseIdx);
                cellDataI.setUpwindCell(intersection.indexInInside(), contiEqIdx, false);
            }
            else
            {
                doUpwinding[phaseIdx] = false;
                cellDataI.setUpwindCell(intersection.indexInInside(), contiEqIdx, false);
                cellDataJ.setUpwindCell(intersection.indexInOutside(), contiEqIdx, false);
            }
        }
        else // Transport after PE with check on flow direction
        {
            bool cellIwasUpwindCell;
            //get the information from smaller (higher level) cell, as its IS is unique
            if(elementI.level()>neighbor.level())
                cellIwasUpwindCell = cellDataI.isUpwindCell(intersection.indexInInside(), contiEqIdx);
            else // reverse neighbors information gathered
                cellIwasUpwindCell = !cellDataJ.isUpwindCell(intersection.indexInOutside(), contiEqIdx);
 
            if (potential[phaseIdx] > 0. && cellIwasUpwindCell)
                lambda[phaseIdx] = cellDataI.mobility(phaseIdx);
            else if (potential[phaseIdx] < 0. && !cellIwasUpwindCell)
                lambda[phaseIdx] = cellDataJ.mobility(phaseIdx);
            // potential direction does not coincide with that of P.E.
            else if(this->restrictFluxInTransport_ == 2)   // perform central averaging for all direction changes
                doUpwinding[phaseIdx] = false;
            else    // i.e. restrictFluxInTransport == 1
            {
               //check if harmonic weithing is necessary
                if (potential[phaseIdx] > 0. && Dune::FloatCmp::ne<Scalar, Dune::FloatCmp::absolute>(cellDataJ.mobility(phaseIdx), 0.0, 1.0e-30)) // check if outflow induce neglected (i.e. mob=0) phase flux
                    lambda[phaseIdx] = cellDataI.mobility(phaseIdx);
                else if (potential[phaseIdx] < 0. && Dune::FloatCmp::ne<Scalar, Dune::FloatCmp::absolute>(cellDataI.mobility(phaseIdx), 0.0, 1.0e-30)) // check if inflow induce neglected phase flux
                    lambda[phaseIdx] = cellDataJ.mobility(phaseIdx);
                else
                    doUpwinding[phaseIdx] = false;
            }
 
            // do not perform upwinding if so desired
            if(!doUpwinding[phaseIdx])
            {
                //a) no flux if there wont be any flux regardless how to average/upwind
                if(cellDataI.mobility(phaseIdx)+cellDataJ.mobility(phaseIdx)==0.)
                {
                    potential[phaseIdx] = 0;
                    continue;
                }
 
                //b) perform harmonic averaging
                fluxEntries[wCompIdx] -= potential[phaseIdx] / volume
                        * harmonicMean(cellDataI.massFraction(phaseIdx, wCompIdx) * cellDataI.mobility(phaseIdx) * cellDataI.density(phaseIdx),
                                cellDataJ.massFraction(phaseIdx, wCompIdx) * cellDataJ.mobility(phaseIdx) * cellDataJ.density(phaseIdx));
                fluxEntries[nCompIdx] -= potential[phaseIdx] / volume
                        * harmonicMean(cellDataI.massFraction(phaseIdx, nCompIdx) * cellDataI.mobility(phaseIdx) * cellDataI.density(phaseIdx),
                                cellDataJ.massFraction(phaseIdx, nCompIdx) * cellDataJ.mobility(phaseIdx) * cellDataJ.density(phaseIdx));
                // c) timestep control
                // for timestep control : influx
                using std::max;
                timestepFlux[0] += max(0.,
                        - potential[phaseIdx] / volume
                          * harmonicMean(cellDataI.mobility(phaseIdx),cellDataJ.mobility(phaseIdx)));
                // outflux
                timestepFlux[1] += max(0.,
                        potential[phaseIdx]  / volume
                        * harmonicMean(cellDataI.mobility(phaseIdx),cellDataJ.mobility(phaseIdx))/SmobI[phaseIdx]);
 
                //d) output (only for one side)
                this->averagedFaces_++;
                #if DUNE_MINIMAL_DEBUG_LEVEL < 3
                // verbose (only for one side)
                if(globalIdxI > globalIdxJ)
                    Dune::dinfo << "harmonicMean flux of phase" << phaseIdx <<" used from cell" << globalIdxI<< " into " << globalIdxJ
                    << " ; TE upwind I = "<< cellIwasUpwindCell << " but pot = "<< potential[phaseIdx] <<  std::endl;
                #endif
 
                //e) stop further standard calculations
                potential[phaseIdx] = 0;
            }
        }
    }
 
    // calculate and standardized velocity
    using std::max;
    double velocityJIw = max((-lambda[wPhaseIdx] * potential[wPhaseIdx]) / volume, 0.0);
    double velocityIJw = max(( lambda[wPhaseIdx] * potential[wPhaseIdx]) / volume, 0.0);
    double velocityJIn = max((-lambda[nPhaseIdx] * potential[nPhaseIdx]) / volume, 0.0);
    double velocityIJn = max(( lambda[nPhaseIdx] * potential[nPhaseIdx]) / volume, 0.0);
 
    // for timestep control
    timestepFlux[0] += velocityJIw + velocityJIn;
 
    double foutw = velocityIJw/SmobI[wPhaseIdx];
    double foutn = velocityIJn/SmobI[nPhaseIdx];
    using std::isnan;
    using std::isinf;
    if (isnan(foutw) || isinf(foutw) || foutw < 0) foutw = 0;
    if (isnan(foutn) || isinf(foutn) || foutn < 0) foutn = 0;
    timestepFlux[1] += foutw + foutn;
 
    fluxEntries[wCompIdx] +=
          velocityJIw * cellDataJ.massFraction(wPhaseIdx, wCompIdx) * densityWJ
        - velocityIJw * cellDataI.massFraction(wPhaseIdx, wCompIdx) * densityWI
        + velocityJIn * cellDataJ.massFraction(nPhaseIdx, wCompIdx) * densityNWJ
        - velocityIJn * cellDataI.massFraction(nPhaseIdx, wCompIdx) * densityNWI;
    fluxEntries[nCompIdx] +=
          velocityJIw * cellDataJ.massFraction(wPhaseIdx, nCompIdx) * densityWJ
        - velocityIJw * cellDataI.massFraction(wPhaseIdx, nCompIdx) * densityWI
        + velocityJIn * cellDataJ.massFraction(nPhaseIdx, nCompIdx) * densityNWJ
        - velocityIJn * cellDataI.massFraction(nPhaseIdx, nCompIdx) * densityNWI;
    return;
}
 
} // end namespace Dumux
#endif