test/porousmediumflow/richards/implicit/analytical/problem.hh

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#ifndef DUMUX_RICHARDS_ANALYTICALPROBLEM_HH
#define DUMUX_RICHARDS_ANALYTICALPROBLEM_HH
 
#include <cmath>
#include <dune/geometry/quadraturerules.hh>
#include <dune/grid/yaspgrid.hh>
 
#include <dumux/discretization/cctpfa.hh>
#include <dumux/discretization/box.hh>
#include <dumux/porousmediumflow/problem.hh>
 
#include <dumux/porousmediumflow/richards/model.hh>
#include <dumux/material/components/simpleh2o.hh>
#include <dumux/material/fluidsystems/1pliquid.hh>
 
#include "spatialparams.hh"
 
namespace Dumux {
 
template <class TypeTag>
class RichardsAnalyticalProblem;
 
// Specify the properties for the analytical problem
namespace Properties {
// Create new type tags
namespace TTag {
struct RichardsAnalytical { using InheritsFrom = std::tuple<Richards>; };
struct RichardsAnalyticalBox { using InheritsFrom = std::tuple<RichardsAnalytical, BoxModel>; };
struct RichardsAnalyticalCC { using InheritsFrom = std::tuple<RichardsAnalytical, CCTpfaModel>; };
} // end namespace TTag
 
// Use 2d YaspGrid
template<class TypeTag>
struct Grid<TypeTag, TTag::RichardsAnalytical> { using type = Dune::YaspGrid<2>; };
 
// Set the physical problem to be solved
template<class TypeTag>
struct Problem<TypeTag, TTag::RichardsAnalytical> { using type = RichardsAnalyticalProblem<TypeTag>; };
 
// Set the spatial parameters
template<class TypeTag>
struct SpatialParams<TypeTag, TTag::RichardsAnalytical>
{
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using type = RichardsAnalyticalSpatialParams<GridGeometry, Scalar>;
};
} // end namespace Properties
 
template <class TypeTag>
class RichardsAnalyticalProblem :  public PorousMediumFlowProblem<TypeTag>
{
    using ParentType = PorousMediumFlowProblem<TypeTag>;
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
    using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
    using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
    enum {
        // copy some indices for convenience
        pwIdx = Indices::pressureIdx,
        bothPhases = Indices::bothPhases,
    };
    // Grid and world dimension
    static const int dimWorld = GridView::dimensionworld;
    static const int dim = GridView::dimension;
    using Element = typename GridView::template Codim<0>::Entity;
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
    using Geometry = typename GridView::template Codim<0>::Entity::Geometry;
 
public:
    RichardsAnalyticalProblem(std::shared_ptr<const GridGeometry> gridGeometry)
    : ParentType(gridGeometry)
    {
        pnRef_ = 1e5; // air pressure
        name_ = getParam<std::string>("Problem.Name");
        time_ = 0.0;
    }
 
    // \{
 
    const std::string name() const
    { return name_; }
 
    void setTime(Scalar time)
    { time_ = time; }
 
    Scalar temperature() const
    { return 273.15 + 10; } // -> 10°C
 
    Scalar nonWettingReferencePressure() const
    { return pnRef_; }
 
    NumEqVector sourceAtPos(const GlobalPosition &globalPos) const
    {
        NumEqVector values(0.0);
        const Scalar time = time_;
        const Scalar pwTop = 98942.8;
        const Scalar pwBottom = 95641.1;
 
        // linear model with complex solution
        // calculated with Matlab script "Richards.m"
        using std::pow;
        using std::tanh;
 
        values = (pow(tanh(globalPos[1]*5.0+time*(1.0/1.0E1)-1.5E1),2.0)*(1.0/1.0E1)
            -1.0/1.0E1)*(pwBottom*(1.0/2.0)-pwTop*(1.0/2.0))*4.0E-8-((pow(tanh(globalPos[1]
            *5.0+time*(1.0/1.0E1)-1.5E1),2.0)*5.0-5.0)*(pwBottom*(1.0/2.0)-pwTop*(1.0/2.0))-1.0E3)
            *(pow(tanh(globalPos[1]*5.0+time*(1.0/1.0E1)-1.5E1),2.0)*5.0-5.0)*(pwBottom
            *(1.0/2.0)-pwTop*(1.0/2.0))*5.0E-16+tanh(globalPos[1]*5.0+time*(1.0/1.0E1)-1.5E1)
            *(pow(tanh(globalPos[1]*5.0+time*(1.0/1.0E1)-1.5E1),2.0)*5.0-5.0)*(pwBottom
            *(1.0/2.0)-pwTop*(1.0/2.0))*(pwBottom*5.0E-16-(tanh(globalPos[1]*5.0+time*(1.0/1.0E1)
            -1.5E1)+1.0)*(pwBottom*(1.0/2.0)-pwTop*(1.0/2.0))*5.0E-16+4.99995E-6)*1.0E1;
        return values;
    }
 
    // \}
 
    // \{
 
    BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
    {
        BoundaryTypes bcTypes;
        if (onLowerBoundary_(globalPos) ||
            onUpperBoundary_(globalPos))
        {
            bcTypes.setAllDirichlet();
        }
        else
            bcTypes.setAllNeumann();
        return bcTypes;
    }
 
    PrimaryVariables dirichletAtPos(const GlobalPosition &globalPos) const
    {
        PrimaryVariables values(0.0);
        values.setState(bothPhases);
        const Scalar time = time_;
        const Scalar pwTop = 98942.8;
        const Scalar pwBottom = 95641.1;
        using std::tanh;
        Scalar pw = pwBottom
          + 0.5 * (tanh( (5.0 * globalPos[1]) - 15.0 + time/10.0) + 1.0) * (pwTop - pwBottom);
 
        values[pwIdx] = pw;
        return values;
    }
 
    NumEqVector neumannAtPos(const GlobalPosition &globalPos) const
    {
        NumEqVector values(0.0);
        return values;
    }
 
    // \{
 
    PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const
    {
        PrimaryVariables values(0.0);
        values.setState(bothPhases);
        analyticalSolution(values, time_, globalPos);
        return values;
    }
 
    // \}
 
    void analyticalSolution(PrimaryVariables &values,
                            const Scalar time,
                            const GlobalPosition &globalPos) const
    {
 
        const Scalar pwTop = 98942.8;
        const Scalar pwBottom = 95641.1;
        using std::tanh;
        Scalar pw = pwBottom
          + 0.5 * (tanh( (5.0 * globalPos[1]) - 15.0 + time/10.0) + 1.0) * (pwTop - pwBottom);
 
        values[pwIdx] = pw;
    }
 
    Scalar calculateL2Error(const SolutionVector& curSol)
    {
        const unsigned int qOrder = 4;
        Scalar l2error = 0.0;
        Scalar l2analytic = 0.0;
        const Scalar time = time_;
 
        for (const auto& element :elements(this->gridGeometry().gridView()))
        {
            int eIdx = this->gridGeometry().elementMapper().index(element);
            // value from numerical approximation
            Scalar numericalSolution = curSol[eIdx];
 
            // integrate over element using a quadrature rule
            Geometry geometry = element.geometry();
            Dune::GeometryType gt = geometry.type();
            Dune::QuadratureRule<Scalar, dim> rule =
                Dune::QuadratureRules<Scalar, dim>::rule(gt, qOrder);
 
            for (auto qIt = rule.begin(); qIt != rule.end(); ++qIt)
            {
                // evaluate analytical solution
                Dune::FieldVector<Scalar, dim> globalPos = geometry.global(qIt->position());
                PrimaryVariables values(0.0);
                analyticalSolution(values, time, globalPos);
                // add contributino of current quadrature point
                l2error += (numericalSolution - values[0]) * (numericalSolution - values[0]) *
                    qIt->weight() * geometry.integrationElement(qIt->position());
                l2analytic += values[0] * values[0] *
                    qIt->weight() * geometry.integrationElement(qIt->position());
            }
        }
        using std::sqrt;
        return sqrt(l2error/l2analytic);
    }
 
    void writeOutput(const SolutionVector& curSol)
    {
 
        Scalar l2error = calculateL2Error(curSol);
 
        // compute L2 error if analytical solution is available
        std::cout.precision(8);
        std::cout << "L2 error for "
                  << std::setw(6) << this->gridGeometry().gridView().size(0)
                  << " elements: "
                  << std::scientific
                  << l2error
                  << std::endl;
    }
 
private:
 
    // evaluates if global position is at lower boundary
    bool onLowerBoundary_(const GlobalPosition &globalPos) const
    {
        return globalPos[1] < this->gridGeometry().bBoxMin()[1] + eps_;
    }
 
    // evaluates if global position is at upper boundary
    bool onUpperBoundary_(const GlobalPosition &globalPos) const
    {
        return globalPos[1] > this->gridGeometry().bBoxMax()[1] - eps_;
    }
 
    static constexpr Scalar eps_ = 3e-6;
    Scalar pnRef_;
    std::string name_;
    Scalar time_;
};
} // end namespace Dumux
 
#endif