mimetic.hh

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#ifndef DUMUX_MIMETIC2P_HH
#define DUMUX_MIMETIC2P_HH
 
#include<map>
#include<iostream>
#include<iomanip>
#include<fstream>
#include<vector>
#include<sstream>
 
#include<dune/common/exceptions.hh>
#include<dune/grid/common/grid.hh>
#include<dune/geometry/type.hh>
#include<dune/geometry/quadraturerules.hh>
 
#include <dumux/porousmediumflow/2p/sequential/diffusion/properties.hh>
#include <dumux/common/boundaryconditions.hh>
#include "localstiffness.hh"
 
#include <dune/common/dynvector.hh>
 
#include <dumux/common/deprecated.hh>
 
namespace Dumux {
 
template<class TypeTag>
class MimeticTwoPLocalStiffness: public LocalStiffness<TypeTag, 1>
{
    using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
 
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
 
    // grid types
    enum
    {
        dim = GridView::dimension
    };
    enum
    {
        wPhaseIdx = Indices::wPhaseIdx,
        nPhaseIdx = Indices::nPhaseIdx,
        pressureIdx = Indices::pressureIdx,
        saturationIdx = Indices::saturationIdx,
        pressureEqIdx = Indices::pressureEqIdx,
        satEqIdx = Indices::satEqIdx,
        numPhases = getPropValue<TypeTag, Properties::NumPhases>()
    };
    enum
    {
        pw = Indices::pressureW,
        pn = Indices::pressureNw,
        pGlobal = Indices::pressureGlobal,
        Sw = Indices::saturationW,
        Sn = Indices::saturationNw,
        vw = Indices::velocityW,
        vn = Indices::velocityNw,
        pressureType = getPropValue<TypeTag, Properties::PressureFormulation>(),
        saturationType = getPropValue<TypeTag, Properties::SaturationFormulation>()
    };
 
    using Grid = typename GridView::Grid;
    using Element = typename GridView::Traits::template Codim<0>::Entity;
 
    using BoundaryTypes = GetPropType<TypeTag, Properties::SequentialBoundaryTypes>;
    using SolutionTypes = GetProp<TypeTag, Properties::SolutionTypes>;
    using PrimaryVariables = typename SolutionTypes::PrimaryVariables;
    using CellData = GetPropType<TypeTag, Properties::CellData>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using FluidState = GetPropType<TypeTag, Properties::FluidState>;
 
public:
    // define the number of components of your system, this is used outside
    // to allocate the correct size of (dense) blocks with a FieldMatrix
    enum
    {
        m = 1
    };
    enum
    {
        size = 2 * dim
    };
 
    MimeticTwoPLocalStiffness(Problem& problem,  bool levelBoundaryAsDirichlet,
            const GridView& gridView, bool procBoundaryAsDirichlet = true) :
            problem_(problem), gridView_(gridView), maxError_(0), timeStep_(1)
    {
        ErrorTermFactor_ = getParam<Scalar>("Impet.ErrorTermFactor");
        ErrorTermLowerBound_ = getParam<Scalar>("Impet.ErrorTermLowerBound");
        ErrorTermUpperBound_ = getParam<Scalar>("Impet.ErrorTermUpperBound");
 
        density_[wPhaseIdx] = 0.0;
        density_[nPhaseIdx] = 0.0;
        viscosity_[wPhaseIdx] =0.0;
        viscosity_[nPhaseIdx] = 0.0;
    }
 
    void initialize()
    {
        const auto element = *problem_.gridView().template begin<0>();
        FluidState fluidState;
        fluidState.setPressure(wPhaseIdx, problem_.referencePressure(element));
        fluidState.setPressure(nPhaseIdx, problem_.referencePressure(element));
        fluidState.setTemperature(problem_.temperature(element));
        fluidState.setSaturation(wPhaseIdx, 1.);
        fluidState.setSaturation(nPhaseIdx, 0.);
        density_[wPhaseIdx] = FluidSystem::density(fluidState, wPhaseIdx);
        density_[nPhaseIdx] = FluidSystem::density(fluidState, nPhaseIdx);
        viscosity_[wPhaseIdx] = FluidSystem::viscosity(fluidState, wPhaseIdx);
        viscosity_[nPhaseIdx] = FluidSystem::viscosity(fluidState, nPhaseIdx);
 
        int size = gridView_.size(0);
        rhs_.resize(size , 0.);
        W_.resize(size);
    }
 
    void reset()
    {
        rhs_ = 0;
        maxError_ = 0;
        timeStep_ = 1;
    }
 
    void setErrorInfo(Scalar maxErr, Scalar dt)
    {
        maxError_ = maxErr;
        timeStep_ = dt;
    }
 
    void assemble(const Element& element, int k = 1)
    {
        unsigned int numFaces = element.subEntities(1);
        this->setcurrentsize(numFaces);
 
        // clear assemble data
        for (unsigned int i = 0; i < numFaces; i++)
        {
            this->b[i] = 0;
            this->bctype[i].reset();
            for (unsigned int j = 0; j < numFaces; j++)
                this->A[i][j] = 0;
        }
 
        assembleV(element, k);
        assembleBC(element, k);
    }
 
    // TODO/FIXME: this is only valid for linear problems where
    // the local stiffness matrix is independend of the current
    // solution. We need to implement this properly, but this
    // should at least make the thing compile...
    using VBlockType = Dune::FieldVector<Scalar, m>;
    void assemble(const Element &cell, const Dune::BlockVector<VBlockType>& localSolution, int orderOfShapeFns = 1)
    {
        assemble(cell, orderOfShapeFns);
    }
 
    void assembleBoundaryCondition(const Element& element, int k = 1)
    {
        unsigned int numFaces = element.subEntities(1);
        this->setcurrentsize(numFaces);
 
        // clear assemble data
        for (unsigned int i = 0; i < numFaces; i++)
        {
            this->b[i] = 0;
            this->bctype[i].reset();
        }
 
        assembleBC(element, k);
    }
 
    // TODO doc me!
    template<class Vector>
    void completeRHS(const Element& element, Dune::FieldVector<int, 2*dim>& local2Global, Vector& f)
    {
        int eIdxGlobal = problem_.variables().index(element);
        unsigned int numFaces = element.subEntities(1);
 
        Dune::FieldVector<Scalar, 2 * dim> F(0.);
        Scalar dInv = 0.;
        computeReconstructionMatrices(element, W_[eIdxGlobal], F, dInv);
 
        for (unsigned int i = 0; i < numFaces; i++)
        {
            if (!this->bc(i).isDirichlet(pressureEqIdx))
                f[local2Global[i]][0] += (dInv * F[i] * rhs_[eIdxGlobal]);
        }
    }
 
    // TODO doc me!
    Scalar constructPressure(const Element& element, Dune::FieldVector<Scalar,2*dim>& pressTrace)
    {
        int eIdxGlobal = problem_.variables().index(element);
        Scalar volume = element.geometry().volume();
 
        PrimaryVariables sourceVec(0.0);
        problem_.source(sourceVec, element);
        Scalar qmean = volume * (sourceVec[wPhaseIdx]/density_[wPhaseIdx] + sourceVec[nPhaseIdx]/density_[nPhaseIdx]);
        qmean += rhs_[eIdxGlobal];
 
        Dune::FieldVector<Scalar, 2 * dim> F(0.);
        Scalar dInv = 0.;
        computeReconstructionMatrices(element, W_[eIdxGlobal], F, dInv);
 
        return (dInv*(qmean + (F*pressTrace)));
    }
 
    // TODO doc me!
    void constructVelocity(const Element& element, Dune::FieldVector<Scalar,2*dim>& vel,
                           Dune::FieldVector<Scalar,2*dim>& pressTrace, Scalar press)
    {
        int eIdxGlobal = problem_.variables().index(element);
 
        Dune::FieldVector<Scalar, 2 * dim> faceVol(0);
        for (const auto& intersection : intersections(gridView_, element))
        {
            faceVol[intersection.indexInInside()] = intersection.geometry().volume();
        }
 
        vel = 0;
        for (int i = 0; i < 2*dim; i++)
            for (int j = 0; j < 2*dim; j++)
                vel[i] += W_[eIdxGlobal][i][j]*faceVol[j]*(press - pressTrace[j]);
    }
 
    // TODO doc me!
    void constructVelocity(const Element& element, int fIdx, Scalar& vel,
                           Dune::FieldVector<Scalar,2*dim>& pressTrace, Scalar press)
    {
        int eIdxGlobal = problem_.variables().index(element);
 
        Dune::FieldVector<Scalar, 2 * dim> faceVol(0);
        for (const auto& intersection : intersections(gridView_, element))
        {
            faceVol[intersection.indexInInside()] = intersection.geometry().volume();
        }
 
        vel = 0;
            for (int j = 0; j < 2*dim; j++)
                vel += W_[eIdxGlobal][fIdx][j]*faceVol[j]*(press - pressTrace[j]);
    }
 
    // TODO doc me!
    void computeReconstructionMatrices(const Element& element,
                                       const Dune::FieldMatrix<Scalar, 2 * dim, 2 * dim>& W,
                                       Dune::FieldVector<Scalar, 2 * dim>& F, Scalar& dInv)
    {
        Dune::FieldVector<Scalar, 2 * dim> c(0);
        Dune::FieldMatrix<Scalar, 2 * dim, 2 * dim> Pi(0);
 
        for (const auto& intersection : intersections(gridView_, element))
        {
            // local number of facet
            int idx = intersection.indexInInside();
 
            Scalar faceVol = intersection.geometry().volume();
 
            // Corresponding to the element under consideration,
            // calculate the part of the matrix C coupling velocities and element pressures.
            // This is just a row vector of size numFaces.
            // scale with volume
            c[idx] = faceVol;
            // Set up the element part of the matrix \Pi coupling velocities
            // and pressure-traces. This is a diagonal matrix with entries given by faceVol.
            Pi[idx][idx] = faceVol;
        }
 
        // Calculate the element part of the matrix D^{-1} = (c W c^T)^{-1} which is just a scalar value.
        Dune::FieldVector<Scalar, 2 * dim> Wc(0);
        W.umv(c, Wc);
        dInv = 1.0 / (c * Wc);
 
        // Calculate the element part of the matrix F = Pi W c^T which is a column vector.
        F = 0;
        Pi.umv(Wc, F);
    }
 
    void assembleElementMatrices(const Element& element, Dune::FieldVector<Scalar, 2 * dim>& faceVol,
    Dune::FieldVector<Scalar, 2 * dim>& F,
    Dune::FieldMatrix<Scalar, 2 * dim, 2 * dim>& Pi,
    Scalar& dInv,
    Scalar& qmean);
 
 
    const Problem& problem() const
    {
        return problem_;
    }
 
private:
    void assembleV(const Element& element, int k = 1);
 
    void assembleBC(const Element& element, int k = 1);
 
    // TODO doc me!
    Scalar evaluateErrorTerm(CellData& cellData)
    {
        //error term for incompressible models to correct unphysical saturation over/undershoots due to saturation transport
        // error reduction routine: volumetric error is damped and inserted to right hand side
        Scalar sat = 0;
        switch (saturationType)
        {
        case Sw:
            sat = cellData.saturation(wPhaseIdx);
            break;
        case Sn:
            sat = cellData.saturation(nPhaseIdx);
            break;
        default:
            DUNE_THROW(Dune::NotImplemented, "Only saturation formulation Sw and Sn are implemented!");
        }
 
        Scalar error = (sat > 1.0) ? sat - 1.0 : 0.0;
        if (sat < 0.0)
        {
            error = sat;
        }
        error /= timeStep_;
 
        using std::abs;
        Scalar errorAbs = abs(error);
 
        if ((errorAbs * timeStep_ > 1e-6) && (errorAbs > ErrorTermLowerBound_ * maxError_)
                && (!problem_.timeManager().willBeFinished()))
        {
            return ErrorTermFactor_ * error;
        }
        return 0.0;
    }
 
private:
    Problem& problem_;
    GridView gridView_;
    Dune::DynamicVector<Scalar> rhs_;
    std::vector<Dune::FieldMatrix<Scalar, 2 * dim, 2 * dim> > W_;
    Scalar maxError_;
    Scalar timeStep_;
    Scalar ErrorTermFactor_; // Handling of error term: relaxation factor
    Scalar ErrorTermLowerBound_; // Handling of error term: lower bound for error dampening
    Scalar ErrorTermUpperBound_; //S Handling of error term: upper bound for error dampening
 
    Scalar density_[numPhases];
    Scalar viscosity_[numPhases];
};
 
// TODO doc me!
template<class TypeTag>
void MimeticTwoPLocalStiffness<TypeTag>::assembleV(const Element& element, int)
{
    unsigned int numFaces = element.subEntities(1);
    this->setcurrentsize(numFaces);
 
    int eIdxGlobal = problem_.variables().index(element);
 
    // The notation is borrowed from Aarnes/Krogstadt/Lie 2006, Section 3.4.
    // The matrix W developed here corresponds to one element-associated
    // block of the matrix B^{-1} there.
    Dune::FieldVector<Scalar, 2 * dim> faceVol(0);
    Dune::FieldMatrix<Scalar, 2 * dim, 2 * dim> Pi(0.);
    Dune::FieldVector<Scalar, 2 * dim> F(0.);
    Scalar dInv = 0.;
    Scalar qmean = 0.;
    this->assembleElementMatrices(element, faceVol, F, Pi, dInv, qmean);
 
    // Calculate the element part of the matrix Pi W Pi^T.
    Dune::FieldMatrix<Scalar, 2 * dim, 2 * dim> PiWPiT(W_[eIdxGlobal]);
    PiWPiT.rightmultiply(Pi);
    PiWPiT.leftmultiply(Pi);
 
    // Calculate the element part of the matrix F D^{-1} F^T.
    Dune::FieldMatrix<Scalar, 2 * dim, 2 * dim> FDinvFT(0);
    for (unsigned int i = 0; i < numFaces; i++)
        for (unsigned int j = 0; j < numFaces; j++)
            FDinvFT[i][j] = dInv * F[i] * F[j];
 
    // Calculate the element part of the matrix S = Pi W Pi^T - F D^{-1} F^T.
    for (unsigned int i = 0; i < numFaces; i++)
        for (unsigned int j = 0; j < numFaces; j++)
            this->A[i][j] = PiWPiT[i][j] - FDinvFT[i][j];
 
    // Calculate the source term F D^{-1} f
    // NOT WORKING AT THE MOMENT
    Scalar factor = dInv * qmean;
    for (unsigned int i = 0; i < numFaces; i++)
        this->b[i] = F[i] * factor;
 
    //        std::cout << "faceVol = " << faceVol << std::endl << "W = " << std::endl << W << std::endl
    //              << "c = " << c << std::endl << "Pi = " << std::endl << Pi << std::endl
    //              << "dinv = " << dinv << std::endl << "F = " << F << std::endl;
    //        std::cout << "dinvF = " << dinvF << ", q = " << qmean
    //             << ", b = " << this->b[0] << ", " << this->b[1] << ", " << this->b[2] << ", " << this->b[3] << std::endl;
}
 
// TODO doc me!
template<class TypeTag>
void MimeticTwoPLocalStiffness<TypeTag>::assembleElementMatrices(const Element& element,
        Dune::FieldVector<Scalar, 2 * dim>& faceVol,
        Dune::FieldVector<Scalar, 2 * dim>& F,
        Dune::FieldMatrix<Scalar, 2 * dim, 2 * dim>& Pi,
        Scalar& dInv,
        Scalar& qmean)
{
    unsigned int numFaces = element.subEntities(1);
    this->setcurrentsize(numFaces);
 
    // get global coordinate of cell center
    Dune::FieldVector<Scalar, dim> centerGlobal = element.geometry().center();
 
    int eIdxGlobal = problem_.variables().index(element);
 
    CellData& cellData = problem_.variables().cellData(eIdxGlobal);
 
    // cell volume
    Scalar volume = element.geometry().volume();
 
    // build the matrices R and ~N
    Dune::FieldMatrix<Scalar, 2 * dim, dim> R(0), N(0);
 
    //       std::cout << "element " << elemId << ": center " << centerGlobal << std::endl;
 
    // collect information needed for calculation of fluxes due to capillary-potential (pc + gravity!)
    Scalar gravPotFace[2*dim];
 
    Scalar gravPot = (problem_.bBoxMax() - centerGlobal) * problem_.gravity() * (density_[nPhaseIdx] - density_[wPhaseIdx]);
 
    for (const auto& intersection : intersections(gridView_, element))
    {
        // local number of facet
        int fIdx = intersection.indexInInside();
 
        Dune::FieldVector<Scalar, dim> faceGlobal = intersection.geometry().center();
        faceVol[fIdx] = intersection.geometry().volume();
 
        // get normal vector
        const Dune::FieldVector<Scalar, dim>& unitOuterNormal = intersection.centerUnitOuterNormal();
 
        N[fIdx] = unitOuterNormal;
 
        for (int k = 0; k < dim; k++)
            // move origin to the center of gravity
            R[fIdx][k] = faceVol[fIdx] * (faceGlobal[k] - centerGlobal[k]);
 
        gravPotFace[fIdx] = (problem_.bBoxMax() - faceGlobal) * problem_.gravity() * (density_[nPhaseIdx] - density_[wPhaseIdx]);
    }
 
    // proceed along the lines of Algorithm 1 from
    // Brezzi/Lipnikov/Simonicini M3AS 2005
    // (1) orthonormalize columns of the matrix R
    Scalar norm = R[0][0] * R[0][0];
    using std::sqrt;
    for (unsigned int i = 1; i < numFaces; i++)
        norm += R[i][0] * R[i][0];
    norm = sqrt(norm);
    for (unsigned int i = 0; i < numFaces; i++)
        R[i][0] /= norm;
    Scalar weight = R[0][1] * R[0][0];
    for (unsigned int i = 1; i < numFaces; i++)
        weight += R[i][1] * R[i][0];
    for (unsigned int i = 0; i < numFaces; i++)
        R[i][1] -= weight * R[i][0];
    norm = R[0][1] * R[0][1];
    for (unsigned int i = 1; i < numFaces; i++)
        norm += R[i][1] * R[i][1];
    norm = sqrt(norm);
    for (unsigned int i = 0; i < numFaces; i++)
        R[i][1] /= norm;
    if (dim == 3)
    {
        Scalar weight1 = R[0][2] * R[0][0];
        Scalar weight2 = R[0][2] * R[0][1];
        for (unsigned int i = 1; i < numFaces; i++)
        {
            weight1 += R[i][2] * R[i][0];
            weight2 += R[i][2] * R[i][1];
        }
        for (unsigned int i = 0; i < numFaces; i++)
            R[i][2] -= weight1 * R[i][0] + weight2 * R[i][1];
        norm = R[0][2] * R[0][2];
        for (unsigned int i = 1; i < numFaces; i++)
            norm += R[i][2] * R[i][2];
        using std::sqrt;
        norm = sqrt(norm);
        for (unsigned int i = 0; i < numFaces; i++)
            R[i][2] /= norm;
    }
    //      std::cout << "~R =\dim" << R;
 
    // (2) Build the matrix ~D
    Dune::FieldMatrix<Scalar, 2 * dim, 2 * dim> D(0);
    for (unsigned int s = 0; s < numFaces; s++)
    {
        Dune::FieldVector<Scalar, 2 * dim> es(0);
        es[s] = 1;
        for (unsigned int k = 0; k < numFaces; k++)
        {
            D[k][s] = es[k];
            for (unsigned int i = 0; i < dim; i++)
            {
                D[k][s] -= R[s][i] * R[k][i];
            }
        }
    }
 
//    std::cout<<"D = "<<D<<"\n";
 
    // eval diffusion tensor, ASSUMING to be constant over each cell
    Dune::FieldMatrix<Scalar, dim, dim> mobility(problem_.spatialParams().intrinsicPermeability(element));
    mobility *= (cellData.mobility(wPhaseIdx) + cellData.mobility(nPhaseIdx));
 
    Scalar traceMob = mobility[0][0];
    for (int i = 1; i < dim; i++)
        traceMob += mobility[i][i];
    D *= 2.0 * traceMob / volume;
    //      std::cout << "u~D =\dim" << D;
 
    // (3) Build the matrix W = Minv
    Dune::FieldMatrix<Scalar, 2 * dim, dim> NK(N);
    NK.rightmultiply(mobility);
 
    for (unsigned int i = 0; i < numFaces; i++)
    {
        for (unsigned int j = 0; j < numFaces; j++)
        {
            W_[eIdxGlobal][i][j] = NK[i][0] * N[j][0];
            for (unsigned int k = 1; k < dim; k++)
                W_[eIdxGlobal][i][j] += NK[i][k] * N[j][k];
        }
    }
 
    W_[eIdxGlobal] /= volume;
    W_[eIdxGlobal] += D;
 
    //       std::cout << "W = \dim" << W;
 
    // Now the notation is borrowed from Aarnes/Krogstadt/Lie 2006, Section 3.4.
    // The matrix W developed so far corresponds to one element-associated
    // block of the matrix B^{-1} there.
 
    // Corresponding to the element under consideration,
    // calculate the part of the matrix C coupling velocities and element pressures.
    // This is just a row vector of size numFaces.
    // scale with volume
    Dune::FieldVector<Scalar, 2 * dim> c(0);
    for (unsigned int i = 0; i < numFaces; i++)
        c[i] = faceVol[i];
 
    // Set up the element part of the matrix \Pi coupling velocities
    // and pressure-traces. This is a diagonal matrix with entries given by faceVol.
    for (unsigned int i = 0; i < numFaces; i++)
        Pi[i][i] = faceVol[i];
 
    // Calculate the element part of the matrix D^{-1} = (c W c^T)^{-1} which is just a scalar value.
    Dune::FieldVector<Scalar, 2 * dim> Wc(0);
    W_[eIdxGlobal].umv(c, Wc);
    dInv = 1.0 / (c * Wc);
 
    // Calculate the element part of the matrix F = Pi W c^T which is a column vector.
    F = 0;
    Pi.umv(Wc, F);
    //      std::cout << "Pi = \dim" << Pi << "c = " << c << ", F = " << F << std::endl;
 
    // accumulate fluxes due to capillary potential (pc + gravity!)
    for (const auto& intersection : intersections(gridView_, element))
    {
        int idx = intersection.indexInInside();
 
        Scalar fracFlow = 0;
 
        Scalar flux = 0;
        for (int j = 0; j < 2 * dim; j++)
            flux += W_[eIdxGlobal][idx][j] * faceVol[j] * (gravPot - gravPotFace[j]);
 
        //it is enough to evaluate the capillary/gravity flux for neighbors -> not needed anyway at the boundaries!
        if (intersection.neighbor())
        {
            int eIdxGlobalNeighbor = problem_.variables().index(intersection.outside());
            if (flux >= 0.)
            {
                switch (pressureType)
                {
                case pw:
                {
                    fracFlow = cellData.fracFlowFunc(nPhaseIdx);
                    break;
                }
                case pn:
                {
                    fracFlow = -cellData.fracFlowFunc(wPhaseIdx);
                    break;
                }
                default:
                    DUNE_THROW(Dune::NotImplemented, "Only pressure formulation pw and pn are implemented!");
                }
 
 
                rhs_[eIdxGlobal] -= (faceVol[idx] * fracFlow * flux);
                rhs_[eIdxGlobalNeighbor] += (faceVol[idx] * fracFlow * flux);
            }
        }
        else if (intersection.boundary())
        {
            BoundaryTypes bctype;
            problem_.boundaryTypes(bctype, intersection);
 
            if (bctype.isDirichlet(pressureEqIdx))
            {
                if (flux > 0. || !bctype.isDirichlet(satEqIdx))
                {
                    switch (pressureType)
                    {
                    case pw:
                    {
                        fracFlow = cellData.fracFlowFunc(nPhaseIdx);
                        break;
                    }
                    case pn:
                    {
                        fracFlow = -cellData.fracFlowFunc(wPhaseIdx);
                        break;
                    }
                    default:
                        DUNE_THROW(Dune::NotImplemented, "Only pressure formulation pw and pn are implemented!");
                    }
                }
                else if (flux < 0. && bctype.isDirichlet(satEqIdx))
                {
                    PrimaryVariables boundValues(0.0);
                    problem_.dirichlet(boundValues, intersection);
 
                    // old material law interface is deprecated: Replace this by
                    // const auto& fluidMatrixInteraction = spatialParams.fluidMatrixInteractionAtPos(element.geometry().center());
                    // after the release of 3.3, when the deprecated interface is no longer supported
                    const auto fluidMatrixInteraction = Deprecated::makePcKrSw(Scalar{}, problem_.spatialParams(), element);
 
                    const Scalar krw = fluidMatrixInteraction.krw(boundValues[saturationIdx]);
                    const Scalar krn = fluidMatrixInteraction.krn(boundValues[saturationIdx]);
 
                    switch (pressureType)
                    {
                    case pw:
                    {
                        fracFlow = krn / viscosity_[nPhaseIdx]
                                / (krw / viscosity_[wPhaseIdx] + krn / viscosity_[nPhaseIdx]);
                        break;
                    }
                    case pn:
                    {
                        fracFlow = -krw / viscosity_[wPhaseIdx]
                                / (krw / viscosity_[wPhaseIdx] + krn / viscosity_[nPhaseIdx]);
                        break;
                    }
                    default:
                        DUNE_THROW(Dune::NotImplemented, "Only pressure formulation pw and pn are implemented!");
                    }
                }
 
                rhs_[eIdxGlobal] -= (faceVol[idx] * fracFlow * flux);
            }
        }
    }
 
    PrimaryVariables sourceVec(0.0);
    problem_.source(sourceVec, element);
    qmean = volume * (sourceVec[wPhaseIdx]/density_[wPhaseIdx] + sourceVec[nPhaseIdx]/density_[nPhaseIdx]);
 
        qmean += evaluateErrorTerm(cellData) * volume;
}
 
// TODO doc me!
template<class TypeTag>
void MimeticTwoPLocalStiffness<TypeTag>::assembleBC(const Element& element, int k)
{
    // evaluate boundary conditions via intersection iterator
    for (const auto& intersection : intersections(gridView_, element))
    {
        int faceIndex = intersection.indexInInside();
        if (intersection.boundary())
        {
            problem_.boundaryTypes(this->bctype[faceIndex], intersection);
            PrimaryVariables boundValues(0.0);
 
            if (this->bctype[faceIndex].isNeumann(pressureEqIdx))
            {
                problem_.neumann(boundValues, intersection);
                Scalar J = (boundValues[wPhaseIdx]/density_[wPhaseIdx] + boundValues[nPhaseIdx]/density_[nPhaseIdx]);
                this->b[faceIndex] -= J * intersection.geometry().volume();
            }
            else if (this->bctype[faceIndex].isDirichlet(pressureEqIdx))
            {
                problem_.dirichlet(boundValues, intersection);
                if (pressureType == pw)
                    this->b[faceIndex] = boundValues[pressureIdx] +
                    (problem_.bBoxMax() - intersection.geometry().center()) * problem_.gravity() * density_[wPhaseIdx];
                else if (pressureType == pn)
                    this->b[faceIndex] = boundValues[pressureIdx] +
                    (problem_.bBoxMax() - intersection.geometry().center()) * problem_.gravity() * density_[nPhaseIdx];
                else
                    this->b[faceIndex] = boundValues[pressureIdx];
            }
        }
    }
 
}
 
}
#endif