freeflowsubproblem.hh

// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
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/*!
 * \file
 * \brief The free flow sub problem
 */
#ifndef DUMUX_STOKES_SUBPROBLEM_HH
#define DUMUX_STOKES_SUBPROBLEM_HH

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

namespace Dumux {

/*!
 * \brief The free flow sub problem
 */
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 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 GlobalPosition = typename Element::Geometry::GlobalCoordinate;

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

    using CouplingManager = GetPropType<TypeTag, Properties::CouplingManager>;

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

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

   /*!
     * \brief Return the temperature within the domain in [K].
     *
     * This problem assumes a temperature of 10 degrees Celsius.
     */
    Scalar temperature() const
    { return 273.15 + 10; } // 10°C

   /*!
     * \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.dofPosition();

        // TODO: dumux-course-task 1.A
        // Change the boundary conditions here as described in the exercise
        if(onUpperBoundary_(globalPos))
        {
            values.setDirichlet(Indices::velocityXIdx);
            values.setDirichlet(Indices::velocityYIdx);
        }

        // left/right wall
        if (onRightBoundary_(globalPos) || (onLeftBoundary_(globalPos)))
        {
            values.setDirichlet(Indices::velocityXIdx);
            values.setDirichlet(Indices::velocityYIdx);
        }

        // coupling interface
        if(couplingManager().isCoupledEntity(CouplingManager::stokesIdx, scvf))
        {
            values.setCouplingNeumann(Indices::conti0EqIdx);
            values.setCouplingNeumann(Indices::momentumYBalanceIdx);
            // TODO: dumux-course-task 1.B
            // Replace Dirichlet BC with Beavers-Joseph-Saffman slip condition for the tangential momentum balance
            values.setDirichlet(Indices::velocityXIdx); // assume no slip on interface

            // TODO: dumux-course-task 1.C
            // set the Beaver-Joseph-Saffman slip condition for the tangential momentum balance equation,
            // consider orientation of face automatically

        }

        return values;
    }

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

        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
     */
    template<class ElementVolumeVariables, class ElementFaceVariables>
    NumEqVector neumann(const Element& element,
                        const FVElementGeometry& fvGeometry,
                        const ElementVolumeVariables& elemVolVars,
                        const ElementFaceVariables& elemFaceVars,
                        const SubControlVolumeFace& scvf) const
    {
        NumEqVector values(0.0);

        if(couplingManager().isCoupledEntity(CouplingManager::stokesIdx, scvf))
        {
            values[Indices::conti0EqIdx] = couplingManager().couplingData().massCouplingCondition(element, fvGeometry, elemVolVars, elemFaceVars, scvf);
            values[Indices::momentumYBalanceIdx] = couplingManager().couplingData().momentumCouplingCondition(element, fvGeometry, elemVolVars, elemFaceVars, scvf);
        }

        return values;
    }

    // \}

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

    //! 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);
        values[Indices::velocityYIdx] = -1e-6 * globalPos[0] * (this->gridGeometry().bBoxMax()[0] - globalPos[0]);
        // TODO: dumux-course-task 1.A
        // Set fixed pressures on the left and right boundary

        return values;
    }

    /*!
     * \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());
    }

    /*!
     * \brief calculate the analytical velocity in x direction based on Beavers & Joseph (1967)
     */
    void calculateAnalyticalVelocityX() const
    {
        analyticalVelocityX_.resize(this->gridGeometry().gridView().size(0));

        using std::sqrt;
        const Scalar dPdX = -deltaP_ / (this->gridGeometry().bBoxMax()[0] - this->gridGeometry().bBoxMin()[0]);
        static const Scalar mu = FluidSystem::viscosity(temperature(), 1e5);
        static const Scalar alpha = getParam<Scalar>("Darcy.SpatialParams.AlphaBeaversJoseph");
        static const Scalar K = getParam<Scalar>("Darcy.SpatialParams.Permeability");
        static const Scalar sqrtK = sqrt(K);
        const Scalar sigma = (this->gridGeometry().bBoxMax()[1] - this->gridGeometry().bBoxMin()[1])/sqrtK;

        const Scalar uB =  -K/(2.0*mu) * ((sigma*sigma + 2.0*alpha*sigma) / (1.0 + alpha*sigma)) * dPdX;

        for (const auto& element : elements(this->gridGeometry().gridView()))
        {
            const auto eIdx = this->gridGeometry().gridView().indexSet().index(element);
            const Scalar y = element.geometry().center()[1] - this->gridGeometry().bBoxMin()[1];

            const Scalar u = uB*(1.0 + alpha/sqrtK*y) + 1.0/(2.0*mu) * (y*y + 2*alpha*y*sqrtK) * dPdX;
            analyticalVelocityX_[eIdx] = u;
        }
    }

    /*!
     * \brief Get the analytical velocity in x direction
     */
    const std::vector<Scalar>& getAnalyticalVelocityX() const
    {
        if(analyticalVelocityX_.empty())
            calculateAnalyticalVelocityX();
        return analyticalVelocityX_;
    }

    // \}

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_; }

    Scalar eps_;
    Scalar deltaP_;

    std::shared_ptr<CouplingManager> couplingManager_;

    mutable std::vector<Scalar> analyticalVelocityX_;
};

} //end namespace Dumux

#endif