test_diffusionproblem.hh

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#ifndef DUMUX_TEST_2P_PROBLEM_HH
#define DUMUX_TEST_2P_PROBLEM_HH
 
#include <dune/grid/yaspgrid.hh>
#include <dune/grid/utility/structuredgridfactory.hh>
 
#include <dumux/material/components/constant.hh>
 
#include <dumux/porousmediumflow/2p/sequential/diffusion/cellcentered/pressureproperties.hh>
#include <dumux/porousmediumflow/2p/sequential/diffusion/mpfa/omethod/2dpressureproperties.hh>
#include <dumux/porousmediumflow/2p/sequential/diffusion/mimetic/pressureproperties.hh>
#include <dumux/porousmediumflow/2p/sequential/diffusion/problem.hh>
#include <dumux/porousmediumflow/sequential/cellcentered/velocity.hh>
 
#include "test_diffusionspatialparams.hh"
 
namespace Dumux {

template<class TypeTag>
class TestDiffusionProblem;

// Specify the properties
namespace Properties
{
NEW_TYPE_TAG(FVVelocity2PTestTypeTag, INHERITS_FROM(FVPressureTwoP, TestDiffusionSpatialParams));
SET_TYPE_PROP(FVVelocity2PTestTypeTag, Problem, TestDiffusionProblem<TypeTag>);
 
// Set the grid type
SET_TYPE_PROP(FVVelocity2PTestTypeTag, Grid, Dune::YaspGrid<2>);
 
// Set the fluid system
template<class TypeTag>
struct FluidSystem<TypeTag, TTag::FVVelocity2PTestTypeTag>
{
    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
    using WettingPhase = FluidSystems::OnePLiquid<Scalar, Components::Constant<1, Scalar> >;
    using NonwettingPhase = FluidSystems::OnePLiquid<Scalar, Components::Constant<1, Scalar> >;
    using type = FluidSystems::TwoPImmiscible<Scalar, WettingPhase, NonwettingPhase>;
};
 
// set the types for the MPFA-O FV method
NEW_TYPE_TAG(FVMPFAOVelocity2PTestTypeTag, INHERITS_FROM(FvMpfaO2dPressureTwoP, TestDiffusionSpatialParams));
//SET_TYPE_PROP(FVMPFAOVelocity2PTestTypeTag, LinearSolver, ILUnBiCGSTABBackend);
SET_TYPE_PROP(FVMPFAOVelocity2PTestTypeTag, LinearSolver, SSORBiCGSTABBackend);
SET_TYPE_PROP(FVMPFAOVelocity2PTestTypeTag, Problem, TestDiffusionProblem<TypeTag>);
// Set the grid type
SET_TYPE_PROP(FVMPFAOVelocity2PTestTypeTag, Grid, Dune::YaspGrid<2>);
 
// Set the fluid system
template<class TypeTag>
struct FluidSystem<TypeTag, TTag::FVMPFAOVelocity2PTestTypeTag>
{
    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
    using WettingPhase = FluidSystems::OnePLiquid<Scalar, Components::Constant<1, Scalar> >;
    using NonwettingPhase = FluidSystems::OnePLiquid<Scalar, Components::Constant<1, Scalar> >;
    using type = FluidSystems::TwoPImmiscible<Scalar, WettingPhase, NonwettingPhase>;
};
 
// set the types for the mimetic FD method
NEW_TYPE_TAG(MimeticPressure2PTestTypeTag, INHERITS_FROM(MimeticPressureTwoP, TestDiffusionSpatialParams));
SET_TYPE_PROP(MimeticPressure2PTestTypeTag, Problem, TestDiffusionProblem<TypeTag>);
 
// Set the grid type
SET_TYPE_PROP(MimeticPressure2PTestTypeTag, Grid, Dune::YaspGrid<2>);
 
// Set the fluid system
template<class TypeTag>
struct FluidSystem<TypeTag, TTag::MimeticPressure2PTestTypeTag>
{
    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
    using WettingPhase = FluidSystems::OnePLiquid<Scalar, Components::Constant<1, Scalar> >;
    using NonwettingPhase = FluidSystems::OnePLiquid<Scalar, Components::Constant<1, Scalar> >;
    using type = FluidSystems::TwoPImmiscible<Scalar, WettingPhase, NonwettingPhase>;
};
 
} // end namespace Properties

template<class TypeTag>
class TestDiffusionProblem: public DiffusionProblem2P<TypeTag>
{
    using ParentType = DiffusionProblem2P<TypeTag>;
    using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
    using Grid = typename GridView::Grid;
 
    using Indices = typename GET_PROP_TYPE(TypeTag, ModelTraits)::Indices;
 
    using WettingPhase = typename GET_PROP(TypeTag, FluidSystem)::WettingPhase;
 
    using BoundaryTypes = typename GET_PROP_TYPE(TypeTag, BoundaryTypes);
 
    enum
    {
        dim = GridView::dimension, dimWorld = GridView::dimensionworld
    };
 
    enum
    {
        wPhaseIdx = Indices::wPhaseIdx,
        pwIdx = Indices::pwIdx,
        swIdx = Indices::swIdx
    };
 
    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
 
    using Element = typename GridView::Traits::template Codim<0>::Entity;
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
    using LocalPosition = Dune::FieldVector<Scalar, dim>;
 
public:
    using SolutionTypes = typename GET_PROP(TypeTag, SolutionTypes);
    using PrimaryVariables = typename SolutionTypes::PrimaryVariables;
    using ScalarSolution = typename SolutionTypes::ScalarSolution;
 
    TestDiffusionProblem(Grid& grid) :
        ParentType(grid), velocity_(*this)
    {
        delta_ = getParam<Scalar>("Problem.Delta", 1e-3);
    }

    void init()
    {
        this->variables().initialize();
        this->spatialParams().initialize(delta_);
        for (int i = 0; i < this->gridView().size(0); i++)
        {
            this->variables().cellData(i).setSaturation(wPhaseIdx, 1.0);
        }
        this->model().initialize();
        velocity_.initialize();
    }

    // \{
 
    bool shouldWriteRestartFile() const
    { return false; }
 
 
    void calculateFVVelocity()
    {
        velocity_.calculateVelocity();
//        velocity_.addOutputVtkFields(this->resultWriter());
    }

    void addOutputVtkFields()
    {
        ScalarSolution *exactPressure = this->resultWriter().allocateManagedBuffer(this->gridView().size(0));
 
        for(const auto& element : elements(this->gridView()))
        {
            (*exactPressure)[this->elementMapper().index(element)][0] = exact(element.geometry().center());
        }
 
        this->resultWriter().attachCellData(*exactPressure, "exact pressure");
 
        this->spatialParams().addOutputVtkFields(this->resultWriter());
 
        return;
    }

    Scalar temperatureAtPos(const GlobalPosition& globalPos) const
    {
        return 273.15 + 10; // -> 10°C
    }
 
    // \}
 

    Scalar referencePressureAtPos(const GlobalPosition& globalPos) const
    {
        return 1e5; // -> 10°C
    }
 
    void source(PrimaryVariables &values,const Element& element) const
    {
        values = 0;
 
        values[wPhaseIdx] = integratedSource_(element, 4);
    }

    void boundaryTypesAtPos(BoundaryTypes &bcTypes, const GlobalPosition& globalPos) const
    {
 
          bcTypes.setAllDirichlet();
    }

    void dirichletAtPos(PrimaryVariables &values, const GlobalPosition& globalPos) const
    {
            values[pwIdx] = exact(globalPos);
            values[swIdx] = 1.0;
    }

    void neumannAtPos(PrimaryVariables &values, const GlobalPosition& globalPos) const
    {
        values = 0;
    }
 
    Scalar exact (const GlobalPosition& globalPos) const
    {
        using std::sin;
        using std::atan;
 
        Scalar pi = 4.0*atan(1.0);
 
        return (sin(pi*globalPos[0])*sin(pi*globalPos[1]));
    }
 
    Dune::FieldVector<Scalar,dim> exactGrad (const GlobalPosition& globalPos) const
        {
        Dune::FieldVector<Scalar,dim> grad(0);
        using std::sin;
        using std::cos;
        using std::atan;
 
        Scalar pi = 4.0*atan(1.0);
        grad[0] = pi*cos(pi*globalPos[0])*sin(pi*globalPos[1]);
        grad[1] = pi*cos(pi*globalPos[1])*sin(pi*globalPos[0]);
 
        return grad;
        }
 
private:
 
    Scalar integratedSource_(const Element& element, int integrationPoints) const
    {
        Scalar source = 0.;
        LocalPosition localPos(0.0);
        GlobalPosition globalPos(0.0);
        Scalar halfInterval = 1.0/double(integrationPoints)/2.;
        for (int i = 1; i <= integrationPoints; i++)
        {
            for (int j = 1; j <= integrationPoints; j++)
            {
                localPos[0] = double(i)/double(integrationPoints) - halfInterval;
                localPos[1] = double(j)/double(integrationPoints) - halfInterval;
                globalPos = element.geometry().global(localPos);
                source += 1./(integrationPoints*integrationPoints) * evaluateSource_(globalPos);
            }
        }
 
        return source;
    }
 
    Scalar evaluateSource_(const GlobalPosition& globalPos) const
    {
        Scalar temp = temperatureAtPos(globalPos);
        Scalar referencePress = referencePressureAtPos(globalPos);
 
        using std::sin;
        using std::cos;
        using std::atan;
 
        Scalar pi = 4.0 * atan(1.0);
        Scalar x = globalPos[0];
        Scalar y = globalPos[1];
 
        Scalar dpdx = pi * cos(pi * x) * sin(pi * y);
        Scalar dpdy = pi * sin(pi * x) * cos(pi * y);
        Scalar dppdxx = -pi * pi * sin(pi * x) * sin(pi * y);
        Scalar dppdxy = pi * pi * cos(pi * x) * cos(pi * y);
        Scalar dppdyx = dppdxy;
        Scalar dppdyy = dppdxx;
        Scalar kxx = (delta_* x*x + y*y)/(x*x + y*y);
        Scalar kxy = -(1.0 - delta_) * x * y / (x*x + y*y);
        Scalar kyy = (x*x + delta_*y*y)/(x*x + y*y);
        Scalar dkxxdx = 2 * x * y*y * (delta_ - 1.0)/((x*x + y*y) * (x*x + y*y));
        Scalar dkyydy = 2 * x*x * y * (delta_ - 1.0)/((x*x + y*y) * (x*x + y*y));
        Scalar dkxydx = (1.0 - delta_) * y * (x*x - y*y) /((x*x + y*y) * (x*x + y*y));
        Scalar dkxydy = (1.0 - delta_) * x * (y*y - x*x) /((x*x + y*y) * (x*x + y*y));
 
        Scalar fx = dkxxdx * dpdx + kxx * dppdxx + dkxydx * dpdy + kxy * dppdyx;
        Scalar fy = dkxydy * dpdx + kxy * dppdxy + dkyydy * dpdy + kyy * dppdyy;
 
        return -(fx + fy) / WettingPhase::viscosity(temp, referencePress) * WettingPhase::density(temp, referencePress);
    }
 
    Scalar delta_;
    FVVelocity<TypeTag, typename GET_PROP_TYPE(TypeTag, Velocity) > velocity_;
};
} //end namespace
 
#endif