darcyfluxmodule.hh

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
/*
  This file is part of the Open Porous Media project (OPM).
 
  OPM is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 2 of the License, or
  (at your option) any later version.
 
  OPM is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.
 
  You should have received a copy of the GNU General Public License
  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
 
  Consult the COPYING file in the top-level source directory of this
  module for the precise wording of the license and the list of
  copyright holders.
*/
#ifndef EWOMS_DARCY_FLUX_MODULE_HH
#define EWOMS_DARCY_FLUX_MODULE_HH
 
#include <dune/common/fmatrix.hh>
#include <dune/common/fvector.hh>
 
#include <opm/common/Exceptions.hpp>
 
#include <opm/material/common/Valgrind.hpp>
 
#include <opm/models/common/multiphasebaseparameters.hh>
#include <opm/models/common/multiphasebaseproperties.hh>
#include <opm/models/common/quantitycallbacks.hh>
 
#include <array>
#include <cassert>
#include <cmath>
#include <string>
#include <type_traits>
 
namespace Opm {
 
template <class TypeTag>
class DarcyIntensiveQuantities;
 
template <class TypeTag>
class DarcyExtensiveQuantities;
 
template <class TypeTag>
class DarcyBaseProblem;

template <class TypeTag>
struct DarcyFluxModule
{
    using FluxIntensiveQuantities = DarcyIntensiveQuantities<TypeTag>;
    using FluxExtensiveQuantities = DarcyExtensiveQuantities<TypeTag>;
    using FluxBaseProblem = DarcyBaseProblem<TypeTag>;

    static void registerParameters()
    {}
};

template <class TypeTag>
class DarcyBaseProblem
{};

template <class TypeTag>
class DarcyIntensiveQuantities
{
    using ElementContext = GetPropType<TypeTag, Properties::ElementContext>;
 
protected:
    void update_(const ElementContext&,
                 unsigned,
                 unsigned)
    {}
};

template <class TypeTag>
class DarcyExtensiveQuantities
{
    using ElementContext = GetPropType<TypeTag, Properties::ElementContext>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Evaluation = GetPropType<TypeTag, Properties::Evaluation>;
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using Implementation = GetPropType<TypeTag, Properties::ExtensiveQuantities>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using MaterialLaw = GetPropType<TypeTag, Properties::MaterialLaw>;
 
    enum { dimWorld = GridView::dimensionworld };
    enum { numPhases = getPropValue<TypeTag, Properties::NumPhases>() };
 
    using Toolbox = MathToolbox<Evaluation>;
    using EvalDimVector = Dune::FieldVector<Evaluation, dimWorld>;
    using DimVector = Dune::FieldVector<Scalar, dimWorld>;
    using DimMatrix = Dune::FieldMatrix<Scalar, dimWorld, dimWorld>;
 
public:
    const DimMatrix& intrinsicPermability() const
    { return K_; }

    const EvalDimVector& potentialGrad(unsigned phaseIdx) const
    { return potentialGrad_[phaseIdx]; }

    const EvalDimVector& filterVelocity(unsigned phaseIdx) const
    { return filterVelocity_[phaseIdx]; }

    const Evaluation& volumeFlux(unsigned phaseIdx) const
    { return volumeFlux_[phaseIdx]; }
 
protected:
    short upstreamIndex_(unsigned phaseIdx) const
    { return upstreamDofIdx_[phaseIdx]; }
 
    short downstreamIndex_(unsigned phaseIdx) const
    { return downstreamDofIdx_[phaseIdx]; }

    void calculateGradients_(const ElementContext& elemCtx,
                             unsigned faceIdx,
                             unsigned timeIdx)
    {
        const auto& gradCalc = elemCtx.gradientCalculator();
        PressureCallback<TypeTag> pressureCallback(elemCtx);
 
        const auto& scvf = elemCtx.stencil(timeIdx).interiorFace(faceIdx);
        const auto& faceNormal = scvf.normal();
 
        const unsigned i = scvf.interiorIndex();
        const unsigned j = scvf.exteriorIndex();
        interiorDofIdx_ = static_cast<short>(i);
        exteriorDofIdx_ = static_cast<short>(j);
        const unsigned focusDofIdx = elemCtx.focusDofIndex();
 
        // calculate the "raw" pressure gradient
        for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx) {
            if (!elemCtx.model().phaseIsConsidered(phaseIdx)) {
                Valgrind::SetUndefined(potentialGrad_[phaseIdx]);
                continue;
            }
 
            pressureCallback.setPhaseIndex(phaseIdx);
            gradCalc.calculateGradient(potentialGrad_[phaseIdx],
                                       elemCtx,
                                       faceIdx,
                                       pressureCallback);
            Valgrind::CheckDefined(potentialGrad_[phaseIdx]);
        }
 
        // correct the pressure gradients by the gravitational acceleration
        if (Parameters::Get<Parameters::EnableGravity>()) {
            // estimate the gravitational acceleration at a given SCV face
            // using the arithmetic mean
            const auto& gIn = elemCtx.problem().gravity(elemCtx, i, timeIdx);
            const auto& gEx = elemCtx.problem().gravity(elemCtx, j, timeIdx);
 
            const auto& intQuantsIn = elemCtx.intensiveQuantities(i, timeIdx);
            const auto& intQuantsEx = elemCtx.intensiveQuantities(j, timeIdx);
 
            const auto& posIn = elemCtx.pos(i, timeIdx);
            const auto& posEx = elemCtx.pos(j, timeIdx);
            const auto& posFace = scvf.integrationPos();
 
            // the distance between the centers of the control volumes
            DimVector distVecIn(posIn);
            DimVector distVecEx(posEx);
            DimVector distVecTotal(posEx);
 
            distVecIn -= posFace;
            distVecEx -= posFace;
            distVecTotal -= posIn;
            const Scalar absDistTotalSquared = distVecTotal.two_norm2();
            for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx) {
                if (!elemCtx.model().phaseIsConsidered(phaseIdx)) {
                    continue;
                }
 
                // calculate the hydrostatic pressure at the integration point of the face
                Evaluation pStatIn;
 
                if (std::is_same<Scalar, Evaluation>::value ||
                    interiorDofIdx_ == static_cast<int>(focusDofIdx))
                {
                    const Evaluation& rhoIn = intQuantsIn.fluidState().density(phaseIdx);
                    pStatIn = -rhoIn * (gIn * distVecIn);
                }
                else {
                    const Scalar rhoIn = Toolbox::value(intQuantsIn.fluidState().density(phaseIdx));
                    pStatIn = -rhoIn * (gIn * distVecIn);
                }
 
                // the quantities on the exterior side of the face do not influence the
                // result for the TPFA scheme, so they can be treated as scalar values.
                Evaluation pStatEx;
 
                if (std::is_same<Scalar, Evaluation>::value ||
                    exteriorDofIdx_ == static_cast<int>(focusDofIdx))
                {
                    const Evaluation& rhoEx = intQuantsEx.fluidState().density(phaseIdx);
                    pStatEx = -rhoEx * (gEx * distVecEx);
                }
                else {
                    const Scalar rhoEx = Toolbox::value(intQuantsEx.fluidState().density(phaseIdx));
                    pStatEx = -rhoEx * (gEx * distVecEx);
                }
 
                // compute the hydrostatic gradient between the two control volumes (this
                // gradient exhibitis the same direction as the vector between the two
                // control volume centers and the length (pStaticExterior -
                // pStaticInterior)/distanceInteriorToExterior
                Dune::FieldVector<Evaluation, dimWorld> f(distVecTotal);
                f *= (pStatEx - pStatIn) / absDistTotalSquared;
 
                // calculate the final potential gradient
                for (unsigned dimIdx = 0; dimIdx < dimWorld; ++dimIdx) {
                    potentialGrad_[phaseIdx][dimIdx] += f[dimIdx];
                }
 
                for (unsigned dimIdx = 0; dimIdx < potentialGrad_[phaseIdx].size(); ++dimIdx) {
                    if (!isfinite(potentialGrad_[phaseIdx][dimIdx])) {
                        throw NumericalProblem("Non-finite potential gradient for phase '"
                                               + std::string(FluidSystem::phaseName(phaseIdx)) + "'");
                    }
                }
            }
        }
 
        Valgrind::SetUndefined(K_);
        elemCtx.problem().intersectionIntrinsicPermeability(K_, elemCtx, faceIdx, timeIdx);
        Valgrind::CheckDefined(K_);
 
        for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx) {
            if (!elemCtx.model().phaseIsConsidered(phaseIdx)) {
                Valgrind::SetUndefined(potentialGrad_[phaseIdx]);
                continue;
            }
 
            // determine the upstream and downstream DOFs
            Evaluation tmp = 0.0;
            for (unsigned dimIdx = 0; dimIdx < faceNormal.size(); ++dimIdx) {
                tmp += potentialGrad_[phaseIdx][dimIdx]*faceNormal[dimIdx];
            }
 
            if (tmp > 0) {
                upstreamDofIdx_[phaseIdx] = exteriorDofIdx_;
                downstreamDofIdx_[phaseIdx] = interiorDofIdx_;
            }
            else {
                upstreamDofIdx_[phaseIdx] = interiorDofIdx_;
                downstreamDofIdx_[phaseIdx] = exteriorDofIdx_;
            }
 
            // we only carry the derivatives along if the upstream DOF is the one which
            // we currently focus on
            const auto& up = elemCtx.intensiveQuantities(upstreamDofIdx_[phaseIdx], timeIdx);
            if (upstreamDofIdx_[phaseIdx] == static_cast<int>(focusDofIdx)) {
                mobility_[phaseIdx] = up.mobility(phaseIdx);
            }
            else {
                mobility_[phaseIdx] = Toolbox::value(up.mobility(phaseIdx));
            }
        }
    }

    template <class FluidState>
    void calculateBoundaryGradients_(const ElementContext& elemCtx,
                                     unsigned boundaryFaceIdx,
                                     unsigned timeIdx,
                                     const FluidState& fluidState)
    {
        const auto& gradCalc = elemCtx.gradientCalculator();
        BoundaryPressureCallback<TypeTag, FluidState> pressureCallback(elemCtx, fluidState);
 
        // calculate the pressure gradient
        for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx) {
            if (!elemCtx.model().phaseIsConsidered(phaseIdx)) {
                Valgrind::SetUndefined(potentialGrad_[phaseIdx]);
                continue;
            }
 
            pressureCallback.setPhaseIndex(phaseIdx);
            gradCalc.calculateBoundaryGradient(potentialGrad_[phaseIdx],
                                               elemCtx,
                                               boundaryFaceIdx,
                                               pressureCallback);
            Valgrind::CheckDefined(potentialGrad_[phaseIdx]);
        }
 
        const auto& scvf = elemCtx.stencil(timeIdx).boundaryFace(boundaryFaceIdx);
        const auto i = scvf.interiorIndex();
        interiorDofIdx_ = static_cast<short>(i);
        exteriorDofIdx_ = -1;
        int focusDofIdx = elemCtx.focusDofIndex();
 
        // calculate the intrinsic permeability
        const auto& intQuantsIn = elemCtx.intensiveQuantities(i, timeIdx);
        K_ = intQuantsIn.intrinsicPermeability();
 
        // correct the pressure gradients by the gravitational acceleration
        if (Parameters::Get<Parameters::EnableGravity>()) {
            // estimate the gravitational acceleration at a given SCV face
            // using the arithmetic mean
            const auto& gIn = elemCtx.problem().gravity(elemCtx, i, timeIdx);
            const auto& posIn = elemCtx.pos(i, timeIdx);
            const auto& posFace = scvf.integrationPos();
 
            // the distance between the face center and the center of the control volume
            DimVector distVecIn(posIn);
            distVecIn -= posFace;
            const Scalar absDistSquared = distVecIn.two_norm2();
            const Scalar gTimesDist = gIn * distVecIn;
 
            for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx) {
                if (!elemCtx.model().phaseIsConsidered(phaseIdx)) {
                    continue;
                }
 
                // calculate the hydrostatic pressure at the integration point of the face
                const Evaluation rhoIn = intQuantsIn.fluidState().density(phaseIdx);
                const Evaluation pStatIn = -gTimesDist * rhoIn;
 
                Valgrind::CheckDefined(pStatIn);
                // compute the hydrostatic gradient between the control volume and face integration
                // point. This gradient exhibitis the same direction as the vector between the
                // control volume center and face integration point (-distVecIn / absDist) and the
                // length of the vector is -pStaticIn / absDist. Note that the two negatives become
                // + and the 1 / (absDist * absDist) -> absDistSquared.
                EvalDimVector f(distVecIn);
                f *= pStatIn / absDistSquared;
 
                // calculate the final potential gradient
                for (unsigned dimIdx = 0; dimIdx < dimWorld; ++dimIdx) {
                    potentialGrad_[phaseIdx][dimIdx] += f[dimIdx];
                }
 
                Valgrind::CheckDefined(potentialGrad_[phaseIdx]);
                for (unsigned dimIdx = 0; dimIdx < potentialGrad_[phaseIdx].size(); ++dimIdx) {
                    if (!isfinite(potentialGrad_[phaseIdx][dimIdx])) {
                        throw NumericalProblem("Non-finite potential gradient for phase '"
                                               + std::string(FluidSystem::phaseName(phaseIdx)) + "'");
                    }
                }
            }
        }
 
        // determine the upstream and downstream DOFs
        const auto& faceNormal = scvf.normal();
 
        const auto& matParams = elemCtx.problem().materialLawParams(elemCtx, i, timeIdx);
 
        std::array<Scalar, numPhases> kr;
        MaterialLaw::relativePermeabilities(kr, matParams, fluidState);
        Valgrind::CheckDefined(kr);
 
        for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx) {
            if (!elemCtx.model().phaseIsConsidered(phaseIdx)) {
                continue;
            }
 
            Evaluation tmp = 0.0;
            for (unsigned dimIdx = 0; dimIdx < faceNormal.size(); ++dimIdx) {
                tmp += potentialGrad_[phaseIdx][dimIdx] * faceNormal[dimIdx];
            }
 
            if (tmp > 0) {
                upstreamDofIdx_[phaseIdx] = exteriorDofIdx_;
                downstreamDofIdx_[phaseIdx] = interiorDofIdx_;
            }
            else {
                upstreamDofIdx_[phaseIdx] = interiorDofIdx_;
                downstreamDofIdx_[phaseIdx] = exteriorDofIdx_;
            }
 
            // take the phase mobility from the DOF in upstream direction
            if (upstreamDofIdx_[phaseIdx] < 0) {
                if (interiorDofIdx_ == focusDofIdx) {
                    mobility_[phaseIdx] = kr[phaseIdx] / fluidState.viscosity(phaseIdx);
                }
                else {
                    mobility_[phaseIdx] = Toolbox::value(kr[phaseIdx]) /
                                          Toolbox::value(fluidState.viscosity(phaseIdx));
                }
            }
            else if (upstreamDofIdx_[phaseIdx] != focusDofIdx) {
                mobility_[phaseIdx] = Toolbox::value(intQuantsIn.mobility(phaseIdx));
            }
            else {
                mobility_[phaseIdx] = intQuantsIn.mobility(phaseIdx);
            }
            Valgrind::CheckDefined(mobility_[phaseIdx]);
        }
    }

    void calculateFluxes_(const ElementContext& elemCtx, unsigned scvfIdx, unsigned timeIdx)
    {
        const auto& scvf = elemCtx.stencil(timeIdx).interiorFace(scvfIdx);
        const DimVector& normal = scvf.normal();
        Valgrind::CheckDefined(normal);
 
        for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx) {
            filterVelocity_[phaseIdx] = 0.0;
            volumeFlux_[phaseIdx] = 0.0;
            if (!elemCtx.model().phaseIsConsidered(phaseIdx)) {
                continue;
            }
 
            asImp_().calculateFilterVelocity_(phaseIdx);
            Valgrind::CheckDefined(filterVelocity_[phaseIdx]);
 
            volumeFlux_[phaseIdx] = 0.0;
            for (unsigned i = 0; i < normal.size(); ++i) {
                volumeFlux_[phaseIdx] += filterVelocity_[phaseIdx][i] * normal[i];
            }
        }
    }

    void calculateBoundaryFluxes_(const ElementContext& elemCtx,
                                  unsigned boundaryFaceIdx,
                                  unsigned timeIdx)
    {
        const auto& scvf = elemCtx.stencil(timeIdx).boundaryFace(boundaryFaceIdx);
        const DimVector& normal = scvf.normal();
        Valgrind::CheckDefined(normal);
 
        for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx) {
            if (!elemCtx.model().phaseIsConsidered(phaseIdx)) {
                filterVelocity_[phaseIdx] = 0.0;
                volumeFlux_[phaseIdx] = 0.0;
                continue;
            }
 
            asImp_().calculateFilterVelocity_(phaseIdx);
            Valgrind::CheckDefined(filterVelocity_[phaseIdx]);
            volumeFlux_[phaseIdx] = 0.0;
            for (unsigned i = 0; i < normal.size(); ++i) {
                volumeFlux_[phaseIdx] += filterVelocity_[phaseIdx][i] * normal[i];
            }
        }
    }
 
    void calculateFilterVelocity_(unsigned phaseIdx)
    {
#ifndef NDEBUG
        assert(isfinite(mobility_[phaseIdx]));
        for (unsigned i = 0; i < K_.M(); ++i) {
            for (unsigned j = 0; j < K_.N(); ++j) {
                assert(std::isfinite(K_[i][j]));
            }
        }
#endif
 
        K_.mv(potentialGrad_[phaseIdx], filterVelocity_[phaseIdx]);
        filterVelocity_[phaseIdx] *= - mobility_[phaseIdx];
 
#ifndef NDEBUG
        for (unsigned i = 0; i < filterVelocity_[phaseIdx].size(); ++i) {
            assert(isfinite(filterVelocity_[phaseIdx][i]));
        }
#endif
    }
 
private:
    Implementation& asImp_()
    { return *static_cast<Implementation*>(this); }
 
    const Implementation& asImp_() const
    { return *static_cast<const Implementation*>(this); }
 
protected:
    // intrinsic permeability tensor and its square root
    DimMatrix K_;
 
    // mobilities of all fluid phases [1 / (Pa s)]
    std::array<Evaluation, numPhases> mobility_;
 
    // filter velocities of all phases [m/s]
    std::array<EvalDimVector, numPhases> filterVelocity_;
 
    // the volumetric flux of all fluid phases over the control
    // volume's face [m^3/s / m^2]
    std::array<Evaluation, numPhases> volumeFlux_;
 
    // pressure potential gradients of all phases [Pa / m]
    std::array<EvalDimVector, numPhases> potentialGrad_;
 
    // upstream, downstream, interior and exterior DOFs
    std::array<short, numPhases> upstreamDofIdx_;
    std::array<short, numPhases> downstreamDofIdx_;
    short interiorDofIdx_;
    short exteriorDofIdx_;
};
 
} // namespace Opm
 
#endif