2p/sequential/diffusion/mimetic/pressure.hh

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#ifndef DUMUX_MIMETICPRESSURE2P_HH
#define DUMUX_MIMETICPRESSURE2P_HH
 
#include <dune/common/exceptions.hh>
 
// dumux environment
#include <dumux/porousmediumflow/sequential/mimetic/properties.hh>
#include <dumux/porousmediumflow/sequential/cellcentered/pressure.hh>
#include <dumux/porousmediumflow/2p/sequential/diffusion/mimetic/operator.hh>
#include <dumux/porousmediumflow/2p/sequential/diffusion/mimetic/mimetic.hh>
 
namespace Dumux {

template<class TypeTag> class MimeticPressure2P
{
    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 FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using FluidState = GetPropType<TypeTag, Properties::FluidState>;
 
    enum
    {
        dim = GridView::dimension, dimWorld = GridView::dimensionworld
    };
    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>(),
    };
    enum
    {
        wPhaseIdx = Indices::wPhaseIdx, nPhaseIdx = Indices::nPhaseIdx,
        numPhases = getPropValue<TypeTag, Properties::NumPhases>()
    };
 
    using Element = typename GridView::Traits::template Codim<0>::Entity;
    using Grid = typename GridView::Grid;
 
    using Geometry = typename Element::Geometry;
    using JacobianTransposed = typename Geometry::JacobianTransposed ;
 
    using LocalStiffness = GetPropType<TypeTag, Properties::LocalStiffness>;
    using TraceType = Dune::BlockVector<Dune::FieldVector<Scalar, 1> >;
    using OperatorAssembler = MimeticOperatorAssemblerTwoP<TypeTag>;
 
    using CellData = GetPropType<TypeTag, Properties::CellData>;
    using SolutionTypes = GetProp<TypeTag, Properties::SolutionTypes>;
    using ScalarSolutionType = typename SolutionTypes::ScalarSolution;
 
    using Matrix = GetPropType<TypeTag, Properties::PressureCoefficientMatrix>;
    using Vector = GetPropType<TypeTag, Properties::PressureRHSVector>;
 
    using DimVector = Dune::FieldVector<Scalar, dim>;

    void initializeMatrix();

    void assemble(bool first)
    {
        Scalar timeStep = problem_.timeManager().timeStepSize();
        Scalar maxError = 0.0;
        int size = problem_.gridView().size(0);
        for (int i = 0; i < size; i++)
        {
            Scalar sat = 0;
            using std::max;
            switch (saturationType)
            {
            case sw:
                sat = problem_.variables().cellData(i).saturation(wPhaseIdx);
                break;
            case sn:
                sat = problem_.variables().cellData(i).saturation(nPhaseIdx);
                break;
            default:
                DUNE_THROW(Dune::NotImplemented, "Only saturation formulation sw and sn are implemented!");
            }
            if (sat > 1.0)
            {
                maxError = max(maxError, (sat - 1.0) / timeStep);
            }
            if (sat < 0.0)
            {
                maxError = max(maxError, (-sat) / timeStep);
            }
        }
 
        lstiff_.setErrorInfo(maxError, timeStep);
        A_.assemble(lstiff_, pressTrace_, f_);
        return;
    }

    void solve();
 
    void postprocess()
    {
        A_.calculatePressure(lstiff_, pressTrace_, problem_);
 
        return;
    }
 
public:
    void updateMaterialLaws();

    void initialize(bool solveTwice = true)
    {
        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);
 
        updateMaterialLaws();
        A_.initialize();
        pressTrace_.resize(problem_.gridView().size(1));
        f_.resize(problem_.gridView().size(1));
        lstiff_.initialize();
        lstiff_.reset();
 
        pressTrace_ = 0.0;
        f_ = 0;
 
        assemble(true);
        solve();
        postprocess();
 
        return;
    }

    void updateVelocity()
    {
        updateMaterialLaws();
        postprocess();
    }
 
    // TODO doc me!
    void update()
    {
        lstiff_.reset();
 
        assemble(false);
        solve();
        postprocess();
 
        return;
    }

    template<class MultiWriter>
    void addOutputVtkFields(MultiWriter &writer)
    {
        int size = problem_.gridView().size(0);
        ScalarSolutionType *potential = writer.allocateManagedBuffer(size);
        ScalarSolutionType *pressure = 0;
        ScalarSolutionType *pressureSecond = 0;
        ScalarSolutionType *potentialSecond = 0;
        Dune::BlockVector < DimVector > *velocityWetting = 0;
        Dune::BlockVector < DimVector > *velocityNonwetting = 0;
 
        if (vtkOutputLevel_ > 0)
        {
            pressure = writer.allocateManagedBuffer(size);
            pressureSecond = writer.allocateManagedBuffer(size);
            potentialSecond = writer.allocateManagedBuffer(size);
            velocityWetting = writer.template allocateManagedBuffer<Scalar, dim>(size);
            velocityNonwetting = writer.template allocateManagedBuffer<Scalar, dim>(size);
        }
 
 
            for (const auto& element : elements(problem_.gridView()))
            {
                int eIdxGlobal = problem_.variables().index(element);
                CellData& cellData = problem_.variables().cellData(eIdxGlobal);
 
                if (pressureType == pw)
                {
                    (*potential)[eIdxGlobal] = cellData.potential(wPhaseIdx);
                }
 
                if (pressureType == pn)
                {
                    (*potential)[eIdxGlobal] = cellData.potential(nPhaseIdx);
                }
 
                if (vtkOutputLevel_ > 0)
                {
 
                if (pressureType == pw)
                {
                    (*pressure)[eIdxGlobal] = cellData.pressure(wPhaseIdx);
                    (*potentialSecond)[eIdxGlobal] = cellData.potential(nPhaseIdx);
                    (*pressureSecond)[eIdxGlobal] = cellData.pressure(nPhaseIdx);
                }
 
                if (pressureType == pn)
                {
                    (*pressure)[eIdxGlobal] = cellData.pressure(nPhaseIdx);
                    (*potentialSecond)[eIdxGlobal] = cellData.potential(wPhaseIdx);
                    (*pressureSecond)[eIdxGlobal] = cellData.pressure(wPhaseIdx);
                }
 
                const typename Element::Geometry& geometry = element.geometry();
 
                // get corresponding reference element
                using ReferenceElements = Dune::ReferenceElements<Scalar, dim>;
                const auto refElement = ReferenceElements::general(geometry.type());
 
                const int numberOfFaces=refElement.size(1);
                std::vector<Scalar> fluxW(numberOfFaces,0);
                std::vector<Scalar> fluxNw(numberOfFaces,0);
 
                // run through all intersections with neighbors and boundary
                for (const auto& intersection : intersections(problem_.gridView(), element))
                {
                    int isIndex = intersection.indexInInside();
 
                    fluxW[isIndex] += intersection.geometry().volume()
                        * (intersection.centerUnitOuterNormal() * cellData.fluxData().velocity(wPhaseIdx, isIndex));
                    fluxNw[isIndex] += intersection.geometry().volume()
                        * (intersection.centerUnitOuterNormal() * cellData.fluxData().velocity(nPhaseIdx, isIndex));
                }
 
                // calculate velocity on reference element as the Raviart-Thomas-0
                // interpolant of the fluxes
                Dune::FieldVector<Scalar, dim> refVelocity;
                // simplices
                if (refElement.type().isSimplex()) {
                    for (int dimIdx = 0; dimIdx < dim; dimIdx++)
                    {
                        refVelocity[dimIdx] = -fluxW[dim - 1 - dimIdx];
                        for (int fIdx = 0; fIdx < dim + 1; fIdx++)
                        {
                            refVelocity[dimIdx] += fluxW[fIdx]/(dim + 1);
                        }
                    }
                }
                // cubes
                else if (refElement.type().isCube()){
                    for (int i = 0; i < dim; i++)
                        refVelocity[i] = 0.5 * (fluxW[2*i + 1] - fluxW[2*i]);
                }
                // 3D prism and pyramids
                else {
                    DUNE_THROW(Dune::NotImplemented, "velocity output for prism/pyramid not implemented");
                }
 
                const DimVector& localPos = refElement.position(0, 0);
 
                // get the transposed Jacobian of the element mapping
                const JacobianTransposed jacobianT = geometry.jacobianTransposed(localPos);
 
                // calculate the element velocity by the Piola transformation
                DimVector elementVelocity(0);
                jacobianT.umtv(refVelocity, elementVelocity);
                elementVelocity /= geometry.integrationElement(localPos);
 
                (*velocityWetting)[eIdxGlobal] = elementVelocity;
 
                // calculate velocity on reference element as the Raviart-Thomas-0
                // interpolant of the fluxes
                // simplices
                if (refElement.type().isSimplex()) {
                    for (int dimIdx = 0; dimIdx < dim; dimIdx++)
                    {
                        refVelocity[dimIdx] = -fluxNw[dim - 1 - dimIdx];
                        for (int fIdx = 0; fIdx < dim + 1; fIdx++)
                        {
                            refVelocity[dimIdx] += fluxNw[fIdx]/(dim + 1);
                        }
                    }
                }
                // cubes
                else if (refElement.type().isCube()){
                    for (int i = 0; i < dim; i++)
                        refVelocity[i] = 0.5 * (fluxNw[2*i + 1] - fluxNw[2*i]);
                }
                // 3D prism and pyramids
                else {
                    DUNE_THROW(Dune::NotImplemented, "velocity output for prism/pyramid not implemented");
                }
 
                // calculate the element velocity by the Piola transformation
                elementVelocity = 0;
                jacobianT.umtv(refVelocity, elementVelocity);
                elementVelocity /= geometry.integrationElement(localPos);
 
                (*velocityNonwetting)[eIdxGlobal] = elementVelocity;
                }
            }
 
            if (pressureType == pw)
            {
                writer.attachCellData(*potential, "wetting potential");
            }
 
            if (pressureType == pn)
            {
                writer.attachCellData(*potential, "nonwetting potential");
            }
 
            if (vtkOutputLevel_ > 0)
            {
            if (pressureType == pw)
            {
                writer.attachCellData(*pressure, "wetting pressure");
                writer.attachCellData(*pressureSecond, "nonwetting pressure");
                writer.attachCellData(*potentialSecond, "nonwetting potential");
            }
 
            if (pressureType == pn)
            {
                writer.attachCellData(*pressure, "nonwetting pressure");
                writer.attachCellData(*pressureSecond, "wetting pressure");
                writer.attachCellData(*potentialSecond, "wetting potential");
            }
 
            writer.attachCellData(*velocityWetting, "wetting-velocity", dim);
            writer.attachCellData(*velocityNonwetting, "non-wetting-velocity", dim);
            }
    }

    void serializeEntity(std::ostream &outstream, const Element &element)
    {
        int numFaces = element.subEntities(1);
        for (int i=0; i < numFaces; i++)
        {
            int fIdxGlobal = A_.faceMapper().subIndex(element, i, 1);
            outstream << pressTrace_[fIdxGlobal][0];
        }
    }

    void deserializeEntity(std::istream &instream, const Element &element)
    {
        int numFaces = element.subEntities(1);
        for (int i=0; i < numFaces; i++)
        {
            int fIdxGlobal = A_.faceMapper().subIndex(element, i, 1);
            instream >> pressTrace_[fIdxGlobal][0];
        }
    }

    MimeticPressure2P(Problem& problem) :
    problem_(problem),
    A_(problem.gridView()), lstiff_(problem_, false, problem_.gridView())
    {
        if (pressureType != pw && pressureType != pn)
        {
            DUNE_THROW(Dune::NotImplemented, "Pressure type not supported!");
        }
        if (saturationType != sw && saturationType != sn)
        {
            DUNE_THROW(Dune::NotImplemented, "Saturation type not supported!");
        }
        if (getPropValue<TypeTag, Properties::EnableCompressibility>())
        {
            DUNE_THROW(Dune::NotImplemented, "Compressibility not supported!");
        }
 
        density_[wPhaseIdx] = 0.0;
        density_[nPhaseIdx] = 0.0;
        viscosity_[wPhaseIdx] = 0.0;
        viscosity_[nPhaseIdx] = 0.0;
 
        vtkOutputLevel_ = getParam<int>("Vtk.OutputLevel");
    }
 
private:
    Problem& problem_;
    TraceType pressTrace_; // vector of pressure traces
    TraceType f_;
    OperatorAssembler A_;
    LocalStiffness lstiff_;
 
    Scalar density_[numPhases];
    Scalar viscosity_[numPhases];
 
    int vtkOutputLevel_;
};

template<class TypeTag>
void MimeticPressure2P<TypeTag>::solve()
{
    using Solver = GetPropType<TypeTag, Properties::LinearSolver>;
 
    auto verboseLevelSolver = getParam<int>("LinearSolver.Verbosity", 0);
 
    if (verboseLevelSolver)
    std::cout << "MimeticPressure2P: solve for pressure" << std::endl;
 
    auto solver = getSolver<Solver>(problem_);
    solver.solve(*A_, pressTrace_, f_);
 
    return;
}

template<class TypeTag>
void MimeticPressure2P<TypeTag>::updateMaterialLaws()
{
        // iterate through leaf grid an evaluate c0 at cell center
        for (const auto& element : elements(problem_.gridView()))
        {
            int eIdxGlobal = problem_.variables().index(element);
 
            CellData& cellData = problem_.variables().cellData(eIdxGlobal);
 
            Scalar satW = cellData.saturation(wPhaseIdx);
 
            // initialize mobilities
            Scalar mobilityW = MaterialLaw::krw(problem_.spatialParams().materialLawParams(element), satW)
                    / viscosity_[wPhaseIdx];
            Scalar mobilityNw = MaterialLaw::krn(problem_.spatialParams().materialLawParams(element), satW)
                    / viscosity_[nPhaseIdx];
 
            // initialize mobilities
            cellData.setMobility(wPhaseIdx, mobilityW);
            cellData.setMobility(nPhaseIdx, mobilityNw);
 
            // initialize fractional flow functions
            cellData.setFracFlowFunc(wPhaseIdx, mobilityW / (mobilityW + mobilityNw));
            cellData.setFracFlowFunc(nPhaseIdx, mobilityNw / (mobilityW + mobilityNw));
        }
        return;
}
 
} // end namespace Dumux
#endif