porousmediumflow/richardsextended/volumevariables.hh

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#ifndef DUMUX_RICHARDSEXTENDED_VOLUME_VARIABLES_HH
#define DUMUX_RICHARDSEXTENDED_VOLUME_VARIABLES_HH
 
#include <cassert>
 
#include <dune/common/exceptions.hh>
 
#include <dumux/porousmediumflow/volumevariables.hh>
#include <dumux/porousmediumflow/nonisothermal/volumevariables.hh>
#include <dumux/material/idealgas.hh>
#include <dumux/material/constants.hh>
#include <dumux/material/solidstates/updatesolidvolumefractions.hh>
 
#include "primaryvariableswitch.hh"
 
namespace Dumux {
 
template <class Traits>
class ExtendedRichardsVolumeVariables
: public PorousMediumFlowVolumeVariables<Traits>
, public EnergyVolumeVariables<Traits, ExtendedRichardsVolumeVariables<Traits> >
{
    using ParentType = PorousMediumFlowVolumeVariables<Traits>;
    using EnergyVolVars = EnergyVolumeVariables<Traits, ExtendedRichardsVolumeVariables<Traits> >;
    using Scalar = typename Traits::PrimaryVariables::value_type;
    using PermeabilityType = typename Traits::PermeabilityType;
    using ModelTraits = typename Traits::ModelTraits;
 
    static constexpr int numFluidComps = ParentType::numFluidComponents();
    static constexpr int numPhases = ParentType::numFluidPhases();
 
    using EffDiffModel = typename Traits::EffectiveDiffusivityModel;
 
    // checks if the fluid system uses the Richards model index convention
    static constexpr auto fsCheck = ModelTraits::checkFluidSystem(typename Traits::FluidSystem{});
 
public:
    using FluidSystem = typename Traits::FluidSystem;
    using FluidState = typename Traits::FluidState;
    using SolidState = typename Traits::SolidState;
    using SolidSystem = typename Traits::SolidSystem;
    using Indices = typename Traits::ModelTraits::Indices;
    using PrimaryVariableSwitch = ExtendedRichardsPrimaryVariableSwitch;
 
    static constexpr auto liquidPhaseIdx = Traits::FluidSystem::phase0Idx;
    static constexpr auto gasPhaseIdx = Traits::FluidSystem::phase1Idx;
 
    template<class ElemSol, class Problem, class Element, class Scv>
    void update(const ElemSol &elemSol,
                const Problem &problem,
                const Element &element,
                const Scv& scv)
    {
        ParentType::update(elemSol, problem, element, scv);
 
        const auto fluidMatrixInteraction = problem.spatialParams().fluidMatrixInteraction(element, scv, elemSol);
 
        const auto& priVars = elemSol[scv.localDofIndex()];
        const auto phasePresence = priVars.state();
 
        // precompute the minimum capillary pressure (entry pressure)
        // needed to make sure we don't compute unphysical capillary pressures and thus saturations
        minPc_ = fluidMatrixInteraction.endPointPc();
 
        //update porosity before calculating the effective properties depending on it
        updateSolidVolumeFractions(elemSol, problem, element, scv, solidState_, numFluidComps);
 
        typename FluidSystem::ParameterCache paramCache;
        auto getEffectiveDiffusionCoefficient = [&](int phaseIdx, int compIIdx, int compJIdx)
        {
            return EffDiffModel::effectiveDiffusionCoefficient(*this, phaseIdx, compIIdx, compJIdx);
        };
 
        if (phasePresence == Indices::gasPhaseOnly)
        {
            moleFraction_[liquidPhaseIdx] = 1.0;
            massFraction_[liquidPhaseIdx] = 1.0;
            moleFraction_[gasPhaseIdx] = priVars[Indices::switchIdx];
 
            const auto averageMolarMassGasPhase = (moleFraction_[gasPhaseIdx]*FluidSystem::molarMass(liquidPhaseIdx)) +
            ((1-moleFraction_[gasPhaseIdx])*FluidSystem::molarMass(gasPhaseIdx));
 
            //X_w = x_w* M_w/ M_avg
            massFraction_[gasPhaseIdx] = priVars[Indices::switchIdx]*FluidSystem::molarMass(liquidPhaseIdx)/averageMolarMassGasPhase;
 
            fluidState_.setSaturation(liquidPhaseIdx, 0.0);
            fluidState_.setSaturation(gasPhaseIdx, 1.0);
 
            EnergyVolVars::updateTemperature(elemSol, problem, element, scv, fluidState_, solidState_);
 
            // get pc for sw = 0.0
            const Scalar pc = fluidMatrixInteraction.pc(0.0);
 
            // set the wetting pressure
            fluidState_.setPressure(liquidPhaseIdx, problem.nonwettingReferencePressure() - pc);
            fluidState_.setPressure(gasPhaseIdx, problem.nonwettingReferencePressure());
 
            molarDensity_[liquidPhaseIdx] = FluidSystem::H2O::liquidDensity(temperature(), pressure(liquidPhaseIdx))/FluidSystem::H2O::molarMass();
            molarDensity_[gasPhaseIdx] = IdealGas<Scalar>::molarDensity(temperature(), problem.nonwettingReferencePressure());
 
            // density and viscosity
            paramCache.updateAll(fluidState_);
            fluidState_.setDensity(liquidPhaseIdx, FluidSystem::density(fluidState_, paramCache, liquidPhaseIdx));
            fluidState_.setDensity(gasPhaseIdx, FluidSystem::density(fluidState_, paramCache, gasPhaseIdx));
            fluidState_.setViscosity(liquidPhaseIdx, FluidSystem::viscosity(fluidState_, paramCache, liquidPhaseIdx));
 
            // compute and set the enthalpy
            fluidState_.setEnthalpy(liquidPhaseIdx, EnergyVolVars::enthalpy(fluidState_, paramCache, liquidPhaseIdx));
            fluidState_.setEnthalpy(gasPhaseIdx, EnergyVolVars::enthalpy(fluidState_, paramCache, gasPhaseIdx));
 
            //binary diffusion coefficients
            paramCache.updateAll(fluidState_);
            effectiveDiffCoeff_ = getEffectiveDiffusionCoefficient(gasPhaseIdx,
                                                                   FluidSystem::comp1Idx,
                                                                   FluidSystem::comp0Idx);
        }
        else if (phasePresence == Indices::bothPhases)
        {
            completeFluidState_(elemSol, problem, element, scv, fluidState_, solidState_);
 
            // we want to account for diffusion in the air phase
            // use Raoult to compute the water mole fraction in air
            molarDensity_[liquidPhaseIdx] = FluidSystem::H2O::liquidDensity(temperature(), pressure(liquidPhaseIdx))/FluidSystem::H2O::molarMass();
            molarDensity_[gasPhaseIdx] = IdealGas<Scalar>::molarDensity(temperature(), problem.nonwettingReferencePressure());
            moleFraction_[liquidPhaseIdx] = 1.0;
 
            moleFraction_[gasPhaseIdx] = FluidSystem::H2O::vaporPressure(temperature()) / problem.nonwettingReferencePressure();
 
            const auto averageMolarMassGasPhase = (moleFraction_[gasPhaseIdx]*FluidSystem::molarMass(liquidPhaseIdx)) +
            ((1-moleFraction_[gasPhaseIdx])*FluidSystem::molarMass(gasPhaseIdx));
 
            //X_w = x_w* M_w/ M_avg
            massFraction_[gasPhaseIdx] = moleFraction_[gasPhaseIdx]*FluidSystem::molarMass(liquidPhaseIdx)/averageMolarMassGasPhase;
 
            // binary diffusion coefficients
            paramCache.updateAll(fluidState_);
            effectiveDiffCoeff_ = getEffectiveDiffusionCoefficient(gasPhaseIdx,
                                                                   FluidSystem::comp1Idx,
                                                                   FluidSystem::comp0Idx);
        }
        else if (phasePresence == Indices::liquidPhaseOnly)
        {
            completeFluidState_(elemSol, problem, element, scv, fluidState_, solidState_);
 
            molarDensity_[liquidPhaseIdx] = FluidSystem::H2O::liquidDensity(temperature(), pressure(liquidPhaseIdx))/FluidSystem::H2O::molarMass();
            molarDensity_[gasPhaseIdx] = IdealGas<Scalar>::molarDensity(temperature(), problem.nonwettingReferencePressure());
            moleFraction_[liquidPhaseIdx] = 1.0;
            moleFraction_[gasPhaseIdx] = 0.0;
            massFraction_[liquidPhaseIdx] = 1.0;
            massFraction_[gasPhaseIdx] = 0.0;
 
            // binary diffusion coefficients (none required for liquid phase only)
            effectiveDiffCoeff_ = 0.0;
        }
 
        // specify the other parameters
        relativePermeabilityWetting_ = fluidMatrixInteraction.krw(fluidState_.saturation(liquidPhaseIdx));
        EnergyVolVars::updateSolidEnergyParams(elemSol, problem, element, scv, solidState_);
        permeability_ = problem.spatialParams().permeability(element, scv, elemSol);
        EnergyVolVars::updateEffectiveThermalConductivity();
    }
 
    const FluidState &fluidState() const
    { return fluidState_; }
 
    const SolidState &solidState() const
    { return solidState_; }
 
    Scalar temperature() const
    { return fluidState_.temperature(); }
 
    Scalar porosity() const
    { return solidState_.porosity(); }
 
    const PermeabilityType& permeability() const
    { return permeability_; }
 
    Scalar saturation(const int phaseIdx = liquidPhaseIdx) const
    { return fluidState_.saturation(phaseIdx); }
 
    Scalar density(const int phaseIdx = liquidPhaseIdx) const
    { return fluidState_.density(phaseIdx); }
 
    Scalar pressure(const int phaseIdx = liquidPhaseIdx) const
    { return fluidState_.pressure(phaseIdx); }
 
    Scalar mobility(const int phaseIdx = liquidPhaseIdx) const
    { return relativePermeability(phaseIdx)/fluidState_.viscosity(phaseIdx); }
 
    Scalar viscosity(const int phaseIdx = liquidPhaseIdx) const
    { return phaseIdx == liquidPhaseIdx ? fluidState_.viscosity(liquidPhaseIdx) : 0.0; }
 
    Scalar relativePermeability(const int phaseIdx = liquidPhaseIdx) const
    { return phaseIdx == liquidPhaseIdx ? relativePermeabilityWetting_ : 1.0; }
 
    Scalar capillaryPressure() const
    {
        using std::max;
        return max(minPc_, pressure(gasPhaseIdx) - pressure(liquidPhaseIdx));
    }
 
    Scalar pressureHead(const int phaseIdx = liquidPhaseIdx) const
    { return 100.0 *(pressure(phaseIdx) - pressure(gasPhaseIdx))/density(phaseIdx)/9.81; }
 
    Scalar waterContent(const int phaseIdx = liquidPhaseIdx) const
    { return saturation(phaseIdx) * solidState_.porosity(); }
 
    Scalar moleFraction(const int phaseIdx, const int compIdx) const
    {
        if (compIdx != FluidSystem::comp0Idx)
            DUNE_THROW(Dune::InvalidStateException, "There is only one component for Richards!");
        return moleFraction_[phaseIdx];
    }
 
    Scalar massFraction(const int phaseIdx, const int compIdx) const
    {
        if (compIdx != FluidSystem::comp0Idx)
            DUNE_THROW(Dune::InvalidStateException, "There is only one component for Richards!");
        return massFraction_[phaseIdx];
    }
 
    Scalar molarDensity(const int phaseIdx) const
    {
        return molarDensity_[phaseIdx];
    }
 
    Scalar diffusionCoefficient(int phaseIdx, int compIIdx, int compJIdx) const
    {
        assert(phaseIdx == gasPhaseIdx);
        assert(compIIdx != compJIdx);
        typename FluidSystem::ParameterCache paramCache;
        paramCache.updatePhase(fluidState_, phaseIdx);
        return FluidSystem::binaryDiffusionCoefficient(fluidState_, paramCache, phaseIdx, compIIdx, compJIdx);
    }
 
    Scalar effectiveDiffusionCoefficient(int phaseIdx, int compIIdx, int compJIdx) const
    {
        assert(phaseIdx == gasPhaseIdx);
        assert(compIIdx != compJIdx);
        return effectiveDiffCoeff_;
    }
private:
    template<class ElemSol, class Problem, class Element, class Scv>
    void completeFluidState_(const ElemSol& elemSol,
                             const Problem& problem,
                             const Element& element,
                             const Scv& scv,
                             FluidState& fluidState,
                             SolidState& solidState)
    {
        EnergyVolVars::updateTemperature(elemSol, problem, element, scv, fluidState, solidState);
 
        const auto fluidMatrixInteraction = problem.spatialParams().fluidMatrixInteraction(element, scv, elemSol);
 
        const auto& priVars = elemSol[scv.localDofIndex()];
 
        // set the wetting pressure
        using std::max;
        Scalar minPc = fluidMatrixInteraction.pc(1.0);
        fluidState.setPressure(liquidPhaseIdx, priVars[Indices::pressureIdx]);
        fluidState.setPressure(gasPhaseIdx, max(problem.nonwettingReferencePressure(), fluidState.pressure(liquidPhaseIdx) + minPc));
 
        // compute the capillary pressure to compute the saturation
        // make sure that we the capillary pressure is not smaller than the minimum pc
        // this would possibly return unphysical values from regularized material laws
        using std::max;
        const Scalar pc = max(fluidMatrixInteraction.endPointPc(),
                              problem.nonwettingReferencePressure() - fluidState.pressure(liquidPhaseIdx));
        const Scalar sw = fluidMatrixInteraction.sw(pc);
        fluidState.setSaturation(liquidPhaseIdx, sw);
        fluidState.setSaturation(gasPhaseIdx, 1.0-sw);
 
        // density and viscosity
        typename FluidSystem::ParameterCache paramCache;
        paramCache.updateAll(fluidState);
        fluidState.setDensity(liquidPhaseIdx,
                              FluidSystem::density(fluidState, paramCache, liquidPhaseIdx));
        fluidState.setDensity(gasPhaseIdx,
                              FluidSystem::density(fluidState, paramCache, gasPhaseIdx));
 
        fluidState.setViscosity(liquidPhaseIdx,
                                FluidSystem::viscosity(fluidState, paramCache, liquidPhaseIdx));
 
        // compute and set the enthalpy
        fluidState.setEnthalpy(liquidPhaseIdx, EnergyVolVars::enthalpy(fluidState, paramCache, liquidPhaseIdx));
        fluidState.setEnthalpy(gasPhaseIdx, EnergyVolVars::enthalpy(fluidState, paramCache, gasPhaseIdx));
    }
 
protected:
    FluidState fluidState_; 
    SolidState solidState_;
    Scalar relativePermeabilityWetting_; 
    PermeabilityType permeability_; 
    Scalar minPc_; 
    Scalar moleFraction_[numPhases]; 
    Scalar massFraction_[numPhases]; 
    Scalar molarDensity_[numPhases]; 
 
    // Effective diffusion coefficients for the phases
    Scalar effectiveDiffCoeff_;
 
};
} // end namespace Dumux
 
#endif