test_1pproblem.hh

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#ifndef DUMUX_TEST_1P_PROBLEM_HH
#define DUMUX_TEST_1P_PROBLEM_HH
 
#include <dune/grid/yaspgrid.hh>
 
#include <dumux/material/fluidsystems/1pliquid.hh>
#include <dumux/material/components/constant.hh>
 
#include <dumux/porousmediumflow/1p/sequential/diffusion/cellcentered/pressureproperties.hh>
#include <dumux/porousmediumflow/1p/sequential/diffusion/problem.hh>
#include <dumux/porousmediumflow/sequential/cellcentered/velocity.hh>
 
#include "test_1pspatialparams.hh"
 
namespace Dumux
{
 
template<class TypeTag>
class TestProblemOneP;

// Specify the properties
namespace Properties
{
NEW_TYPE_TAG(TestOneP, INHERITS_FROM(FVPressureOneP));
 
// Set the grid type
SET_TYPE_PROP(TestOneP, Grid, Dune::YaspGrid<2>);
 
// the fluid system
template<class TypeTag>
struct FluidSystem<TypeTag, TTag::TestOneP>
{
    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
    using type = FluidSystems::OnePLiquid<Scalar, Components::Constant<1, Scalar> >;
};
 
// Set the spatial parameters
SET_TYPE_PROP(TestOneP, SpatialParams, TestOnePSpatialParams<TypeTag>);
 
//Set the problem
SET_TYPE_PROP(TestOneP, Problem, TestProblemOneP<TypeTag>);
}

template<class TypeTag>
class TestProblemOneP: public DiffusionProblem1P<TypeTag >
{
    using ParentType = DiffusionProblem1P<TypeTag>;
    using TimeManager = typename GET_PROP_TYPE(TypeTag, TimeManager);
 
    using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
    using Grid = typename GridView::Grid;
 
    using FluidSystem = typename GET_PROP_TYPE(TypeTag, FluidSystem);
 
    using PrimaryVariables = typename GET_PROP_TYPE(TypeTag, PrimaryVariables);
    using BoundaryTypes = typename GET_PROP_TYPE(TypeTag, BoundaryTypes);
 
    enum
    {
        dim = GridView::dimension, dimWorld = GridView::dimensionworld
    };
 
    using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
 
    using Element = typename GridView::Traits::template Codim<0>::Entity;
    using Intersection = typename GridView::Intersection;
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
    using LocalPosition = Dune::FieldVector<Scalar, dim>;
 
 
public:
    TestProblemOneP(TimeManager& timeManager, Grid& grid) :
        ParentType(grid), velocity_(*this)
    {
        delta_ = getParam<Scalar>("Problem.Delta", 1e-3);
 
        this->spatialParams().initialize(delta_);
    }

    // \{

    std::string name() const
    {
        return "test_1p";
    }
 
    bool shouldWriteRestartFile() const
    { return false; }
 
    void addOutputVtkFields()
    {
        velocity_.calculateVelocity();
        velocity_.addOutputVtkFields(this->resultWriter());
    }

    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 = integratedSource_(element, 4);
    }

    void boundaryTypes(BoundaryTypes &bcType,
            const Intersection& intersection) const
    {
        bcType.setAllDirichlet();
    }

    void dirichletAtPos(PrimaryVariables &values,
                        const GlobalPosition &globalPos) const
    {
        values = exact(globalPos);
    }
 

    void neumann(PrimaryVariables &values, const Intersection& intersection) const
    {
        values = 0;
    }
 
private:
    Scalar exact (const GlobalPosition& globalPos) const
    {
        double pi = 4.0*atan(1.0);
        using std::sin;
        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;
        double 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;
    }
 
    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) / FluidSystem::viscosity(temp, referencePress) * FluidSystem::density(temp, referencePress);
    }
 
    double delta_;
    FVVelocity<TypeTag, typename GET_PROP_TYPE(TypeTag, Velocity) > velocity_;
};
} //end namespace
 
#endif