problem_conduction.hh

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#ifndef DUMUX_1PNI_CONDUCTION_PROBLEM_HH
#define DUMUX_1PNI_CONDUCTION_PROBLEM_HH
 
#include <cmath>
#include <dune/grid/yaspgrid.hh>
 
#include <dumux/discretization/elementsolution.hh>
#include <dumux/discretization/box.hh>
#include <dumux/discretization/cctpfa.hh>
#include <dumux/discretization/ccmpfa.hh>
#include <dumux/discretization/box.hh>
#include <dumux/porousmediumflow/1p/model.hh>
#include <dumux/porousmediumflow/problem.hh>
#include <dumux/material/components/h2o.hh>
#include <dumux/material/fluidsystems/1pliquid.hh>
#include <dumux/material/fluidmatrixinteractions/1p/thermalconductivityaverage.hh>
 
#include "spatialparams.hh"
 
namespace Dumux {
 
template <class TypeTag>
class OnePNIConductionProblem;
 
namespace Properties {
// Create new type tags
namespace TTag {
struct OnePNIConduction { using InheritsFrom = std::tuple<OnePNI>; };
struct OnePNIConductionBox { using InheritsFrom = std::tuple<OnePNIConduction, BoxModel>; };
struct OnePNIConductionCCTpfa { using InheritsFrom = std::tuple<OnePNIConduction, CCTpfaModel>; };
struct OnePNIConductionCCMpfa { using InheritsFrom = std::tuple<OnePNIConduction, CCMpfaModel>; };
} // end namespace TTag
 
// Set the grid type
template<class TypeTag>
struct Grid<TypeTag, TTag::OnePNIConduction> { using type = Dune::YaspGrid<2>; };
 
// Set the problem property
template<class TypeTag>
struct Problem<TypeTag, TTag::OnePNIConduction> { using type = OnePNIConductionProblem<TypeTag>; };
 
// Set the fluid system
template<class TypeTag>
struct FluidSystem<TypeTag, TTag::OnePNIConduction>
{
    using type = FluidSystems::OnePLiquid<GetPropType<TypeTag, Properties::Scalar>,
                                          Components::H2O<GetPropType<TypeTag, Properties::Scalar>> >;
};
 
// Set the spatial parameters
template<class TypeTag>
struct SpatialParams<TypeTag, TTag::OnePNIConduction>
{
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using type = OnePNISpatialParams<GridGeometry, Scalar>;
};
}

template <class TypeTag>
class OnePNIConductionProblem : public PorousMediumFlowProblem<TypeTag>
{
    using ParentType = PorousMediumFlowProblem<TypeTag>;
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
    using ThermalConductivityModel = GetPropType<TypeTag, Properties::ThermalConductivityModel>;
    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
    using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
    using IapwsH2O = Components::H2O<Scalar>;
 
    enum { dimWorld = GridView::dimensionworld };
 
    // copy some indices for convenience
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
    enum {
        // indices of the primary variables
        pressureIdx = Indices::pressureIdx,
        temperatureIdx = Indices::temperatureIdx
    };
 
    using Element = typename GridView::template Codim<0>::Entity;
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
 
public:
    OnePNIConductionProblem(std::shared_ptr<const GridGeometry> gridGeometry, const std::string& paramGroup)
    : ParentType(gridGeometry, paramGroup)
    {
        //initialize fluid system
        FluidSystem::init();
 
        name_ = getParam<std::string>("Problem.Name");
        temperatureHigh_ = 300.0;
        temperatureExact_.resize(gridGeometry->numDofs());
    }

    const std::vector<Scalar>& getExactTemperature()
    {
        return temperatureExact_;
    }

    void updateExactTemperature(const SolutionVector& curSol, Scalar time)
    {
        const auto someElement = *(elements(this->gridGeometry().gridView()).begin());
 
        auto someElemSol = elementSolution(someElement, curSol, this->gridGeometry());
        const auto someInitSol = initialAtPos(someElement.geometry().center());
 
        auto someFvGeometry = localView(this->gridGeometry());
        someFvGeometry.bindElement(someElement);
        const auto someScv = *(scvs(someFvGeometry).begin());
 
        VolumeVariables volVars;
        volVars.update(someElemSol, *this, someElement, someScv);
 
        const auto porosity = this->spatialParams().porosity(someElement, someScv, someElemSol);
        const auto densityW = volVars.density();
        const auto heatCapacityW = IapwsH2O::liquidHeatCapacity(someInitSol[temperatureIdx], someInitSol[pressureIdx]);
        const auto densityS = volVars.solidDensity();
        const auto heatCapacityS = volVars.solidHeatCapacity();
        const auto storage = densityW*heatCapacityW*porosity + densityS*heatCapacityS*(1 - porosity);
        const auto effectiveThermalConductivity = ThermalConductivityModel::effectiveThermalConductivity(volVars);
        using std::max;
        time = max(time, 1e-10);
        for (const auto& element : elements(this->gridGeometry().gridView()))
        {
            auto fvGeometry = localView(this->gridGeometry());
            fvGeometry.bindElement(element);
 
            for (auto&& scv : scvs(fvGeometry))
            {
               auto globalIdx = scv.dofIndex();
               const auto& globalPos = scv.dofPosition();
               using std::erf;
               using std::sqrt;
               temperatureExact_[globalIdx] = temperatureHigh_ + (someInitSol[temperatureIdx] - temperatureHigh_)
                                              *erf(0.5*sqrt(globalPos[0]*globalPos[0]*storage/time/effectiveThermalConductivity));
 
            }
        }
    }

    // \{

    const std::string& name() const
    {
        return name_;
    }
    // \}

    // \{

    BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
    {
        BoundaryTypes bcTypes;
 
        if(globalPos[0] < eps_ || globalPos[0] > this->gridGeometry().bBoxMax()[0] - eps_)
            bcTypes.setAllDirichlet();
        else
            bcTypes.setAllNeumann();
 
        return bcTypes;
    }

    PrimaryVariables dirichletAtPos(const GlobalPosition &globalPos) const
    {
        PrimaryVariables priVars(initial_());
        if (globalPos[0] < eps_)
            priVars[temperatureIdx] = temperatureHigh_;
        return priVars;
    }
 
    // \}

    // \{

    PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const
    {
        return initial_();
    }
 
    // \}
 
private:
    // the internal method for the initial condition
    PrimaryVariables initial_() const
    {
        PrimaryVariables priVars(0.0);
        priVars[pressureIdx] = 1.0e5;
        priVars[temperatureIdx] = 290.0;
        return priVars;
    }
 
    Scalar temperatureHigh_;
    static constexpr Scalar eps_ = 1e-6;
    std::string name_;
    std::vector<Scalar> temperatureExact_;
};
 
} // end namespace Dumux
 
#endif // DUMUX_1PNI_CONDUCTION_PROBLEM_HH