freeflowsubproblem.hh

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/*!
 * \file
 * \ingroup NavierStokesTests
 * \brief A simple Stokes test problem for the staggered grid (Navier-)Stokes model.
 */
#ifndef DUMUX_STOKES1P2C_SUBPROBLEM_HH
#define DUMUX_STOKES1P2C_SUBPROBLEM_HH

#include <dumux/freeflow/navierstokes/problem.hh>
#include <dumux/common/properties.hh>

namespace Dumux {

/*!
 * \ingroup NavierStokesTests
 * \brief  Test problem for the one-phase compositional (Navier-) Stokes problem.
 *
 * Horizontal flow from left to right with a parabolic velocity profile.
 */
template <class TypeTag>
class FreeFlowSubProblem : public NavierStokesProblem<TypeTag>
{
    using ParentType = NavierStokesProblem<TypeTag>;

    using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
    using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;

    using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using FVElementGeometry = typename FVGridGeometry::LocalView;
    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
    using Element = typename GridView::template Codim<0>::Entity;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using ElementFaceVariables = typename GetPropType<TypeTag, Properties::GridFaceVariables>::LocalView;
    using FluidState = GetPropType<TypeTag, Properties::FluidState>;

    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;

    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
    using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;

    using CouplingManager = GetPropType<TypeTag, Properties::CouplingManager>;
    using TimeLoopPtr = std::shared_ptr<TimeLoop<Scalar>>;

    static constexpr bool useMoles = GetPropType<TypeTag, Properties::ModelTraits>::useMoles();

    static constexpr auto dim = GetPropType<TypeTag, Properties::ModelTraits>::dim();
    static constexpr auto transportCompIdx = 1;

public:
    FreeFlowSubProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry, std::shared_ptr<CouplingManager> couplingManager)
    : ParentType(fvGridGeometry, "Stokes"), eps_(1e-6), couplingManager_(couplingManager)
    {
        velocity_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.Velocity");
        pressure_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.Pressure");
        moleFraction_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.MoleFraction");
    }

   /*!
     * \name Problem parameters
     */
    // \{

   /*!
     * \brief Return the temperature within the domain in [K].
     */
    Scalar temperature() const
    { return 293.15; }

   /*!
     * \brief Return the sources within the domain.
     *
     * \param globalPos The global position
     */
    NumEqVector sourceAtPos(const GlobalPosition &globalPos) const
    { return NumEqVector(0.0); }

    // \}
   /*!
     * \name Boundary conditions
     */
    // \{

    /*!
     * \brief Specifies which kind of boundary condition should be
     *        used for which equation on a given boundary segment.
     *
     * \param element The finite element
     * \param scvf The sub control volume face
     */
    BoundaryTypes boundaryTypes(const Element& element,
                                const SubControlVolumeFace& scvf) const
    {
        BoundaryTypes values;

        const auto& globalPos = scvf.center();

        if(onLeftBoundary_(globalPos))
        {
            values.setDirichlet(Indices::conti0EqIdx + 1);
            values.setDirichlet(Indices::velocityXIdx);
            values.setDirichlet(Indices::velocityYIdx);
        }
        else if(onRightBoundary_(globalPos))
        {
            values.setDirichlet(Indices::pressureIdx);
            values.setOutflow(Indices::conti0EqIdx + 1);
        }
        else
        {
            values.setDirichlet(Indices::velocityXIdx);
            values.setDirichlet(Indices::velocityYIdx);
            values.setNeumann(Indices::conti0EqIdx);
            values.setNeumann(Indices::conti0EqIdx + 1);
        }

        if (couplingManager().isCoupledEntity(CouplingManager::stokesIdx, scvf))
        {
            values.setCouplingNeumann(Indices::conti0EqIdx);
            values.setCouplingNeumann(Indices::conti0EqIdx + 1);
            values.setCouplingNeumann(Indices::momentumYBalanceIdx);
            values.setBeaversJoseph(Indices::momentumXBalanceIdx);
        }

        return values;
    }

    /*!
     * \brief Evaluate the boundary conditions for a Dirichlet control volume.
     *
     * \param element The element
     * \param scvf The subcontrolvolume face
     */
    PrimaryVariables dirichletAtPos(const GlobalPosition& pos) const
    {
        PrimaryVariables values(0.0);
        values = initialAtPos(pos);

        return values;
    }

    /*!
     * \brief Evaluate the boundary conditions for a Neumann control volume.
     *
     * \param element The element for which the Neumann boundary condition is set
     * \param fvGeomentry The fvGeometry
     * \param elemVolVars The element volume variables
     * \param elemFaceVars The element face variables
     * \param scvf The boundary sub control volume face
     */
    NumEqVector neumann(const Element& element,
                        const FVElementGeometry& fvGeometry,
                        const ElementVolumeVariables& elemVolVars,
                        const ElementFaceVariables& elemFaceVars,
                        const SubControlVolumeFace& scvf) const
    {
        PrimaryVariables values(0.0);

        if(couplingManager().isCoupledEntity(CouplingManager::stokesIdx, scvf))
        {
            values[Indices::momentumYBalanceIdx] = couplingManager().couplingData().momentumCouplingCondition(element, fvGeometry, elemVolVars, elemFaceVars, scvf);

            const auto massFlux = couplingManager().couplingData().massCouplingCondition(element, fvGeometry, elemVolVars, elemFaceVars, scvf);
            values[Indices::conti0EqIdx] = massFlux[0];
            values[Indices::conti0EqIdx + 1] = massFlux[1];
        }
        return values;
    }

    // \}

    /*!
     * \brief Set the coupling manager
     */
    void setCouplingManager(std::shared_ptr<CouplingManager> cm)
    { couplingManager_ = cm; }

    /*!
     * \brief Get the coupling manager
     */
    const CouplingManager& couplingManager() const
    { return *couplingManager_; }

   /*!
     * \name Volume terms
     */
    // \{

    /*!
      * \brief Evaluate the initial value for a control volume.
      *
      * \param globalPos The global position
      */
     PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const
     {
         PrimaryVariables values(0.0);

         // This is only an approximation of the actual hydorostatic pressure gradient.
         // Air is compressible (the density depends on pressure), thus the actual
         // vertical pressure profile is non-linear.
         // This discrepancy can lead to spurious flows at the outlet if the inlet
         // velocity is chosen too small.
         FluidState fluidState;
         updateFluidStateForBC_(fluidState, pressure_);
         const Scalar density = FluidSystem::density(fluidState, 0);
         values[Indices::pressureIdx] = pressure_ - density*this->gravity()[1]*(this->gridGeometry().bBoxMax()[1] - globalPos[1]);


         // gravity has negative sign
         values[Indices::conti0EqIdx + 1] = moleFraction_;
         values[Indices::velocityXIdx] = 4.0 * velocity_ * (globalPos[1] - this->gridGeometry().bBoxMin()[1])
                                                         * (this->gridGeometry().bBoxMax()[1] - globalPos[1])
                                                         / (height_() * height_());

         return values;
     }

    void setTimeLoop(TimeLoopPtr timeLoop)
    { timeLoop_ = timeLoop; }

    /*!
     * \brief Returns the intrinsic permeability of required as input parameter for the Beavers-Joseph-Saffman boundary condition
     */
    Scalar permeability(const Element& element, const SubControlVolumeFace& scvf) const
    {
        return couplingManager().couplingData().darcyPermeability(element, scvf);
    }

    /*!
     * \brief Returns the alpha value required as input parameter for the Beavers-Joseph-Saffman boundary condition
     */
    Scalar alphaBJ(const SubControlVolumeFace& scvf) const
    {
        return couplingManager().problem(CouplingManager::darcyIdx).spatialParams().beaversJosephCoeffAtPos(scvf.center());
    }

    // \}

private:
    bool onLeftBoundary_(const GlobalPosition &globalPos) const
    { return globalPos[0] < this->gridGeometry().bBoxMin()[0] + eps_; }

    bool onRightBoundary_(const GlobalPosition &globalPos) const
    { return globalPos[0] > this->gridGeometry().bBoxMax()[0] - eps_; }

    bool onLowerBoundary_(const GlobalPosition &globalPos) const
    { return globalPos[1] < this->gridGeometry().bBoxMin()[1] + eps_; }

    bool onUpperBoundary_(const GlobalPosition &globalPos) const
    { return globalPos[1] > this->gridGeometry().bBoxMax()[1] - eps_; }

    //! \brief updates the fluid state to obtain required quantities for IC/BC
    void updateFluidStateForBC_(FluidState& fluidState, const Scalar pressure) const
    {
        fluidState.setTemperature(temperature());
        fluidState.setPressure(0, pressure);
        fluidState.setSaturation(0, 1.0);
        fluidState.setMoleFraction(0, 1, moleFraction_);
        fluidState.setMoleFraction(0, 0, 1.0 - moleFraction_);

        typename FluidSystem::ParameterCache paramCache;
        paramCache.updatePhase(fluidState, 0);

        const Scalar density = FluidSystem::density(fluidState, paramCache, 0);
        fluidState.setDensity(0, density);

        const Scalar molarDensity = FluidSystem::molarDensity(fluidState, paramCache, 0);
        fluidState.setMolarDensity(0, molarDensity);

        const Scalar enthalpy = FluidSystem::enthalpy(fluidState, paramCache, 0);
        fluidState.setEnthalpy(0, enthalpy);
    }
    // the height of the free-flow domain
    const Scalar height_() const
    { return this->gridGeometry().bBoxMax()[1] - this->gridGeometry().bBoxMin()[1]; }

    Scalar eps_;

    Scalar velocity_;
    Scalar pressure_;
    Scalar moleFraction_;

    TimeLoopPtr timeLoop_;

    std::shared_ptr<CouplingManager> couplingManager_;
};

} //end namespace Dumux

#endif // DUMUX_STOKES1P2C_SUBPROBLEM_HH