test/freeflow/shallowwater/roughchannel/problem.hh

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#ifndef DUMUX_ROUGH_CHANNEL_TEST_PROBLEM_HH
#define DUMUX_ROUGH_CHANNEL_TEST_PROBLEM_HH
 
#include <dune/grid/yaspgrid.hh>
#include <dumux/discretization/cctpfa.hh>
#include "spatialparams.hh"
#include <dumux/common/parameters.hh>
 
#include <dumux/freeflow/shallowwater/model.hh>
#include <dumux/freeflow/shallowwater/problem.hh>
#include <dumux/freeflow/shallowwater/boundaryfluxes.hh>
 
namespace Dumux {
 
template <class TypeTag>
class RoughChannelProblem;
 
// Specify the properties for the problem
namespace Properties {
 
// Create new type tags
namespace TTag {
struct RoughChannel { using InheritsFrom = std::tuple<ShallowWater, CCTpfaModel>; };
} // end namespace TTag
 
template<class TypeTag>
struct Grid<TypeTag, TTag::RoughChannel>
{ using type = Dune::YaspGrid<2, Dune::TensorProductCoordinates<GetPropType<TypeTag, Properties::Scalar>, 2> >; };
 
// Set the problem property
template<class TypeTag>
struct Problem<TypeTag, TTag::RoughChannel>
{ using type = Dumux::RoughChannelProblem<TypeTag>; };
 
// Set the spatial parameters
template<class TypeTag>
struct SpatialParams<TypeTag, TTag::RoughChannel>
{
private:
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using VolumeVariables = typename ElementVolumeVariables::VolumeVariables;
public:
    using type = RoughChannelSpatialParams<GridGeometry, Scalar, VolumeVariables>;
};
 
template<class TypeTag>
struct EnableGridGeometryCache<TypeTag, TTag::RoughChannel>
{ static constexpr bool value = true; };
 
template<class TypeTag>
struct EnableGridVolumeVariablesCache<TypeTag, TTag::RoughChannel>
{ static constexpr bool value = false; };
} // end namespace Properties

template <class TypeTag>
class RoughChannelProblem : public ShallowWaterProblem<TypeTag>
{
    using ParentType = ShallowWaterProblem<TypeTag>;
    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
    using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using NeumannFluxes = GetPropType<TypeTag, Properties::NumEqVector>;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
    using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView;
    using VolumeVariables = typename ElementVolumeVariables::VolumeVariables;
    using FVElementGeometry = typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView;
    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using Element = typename GridView::template Codim<0>::Entity;
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
    using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;
    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
 
public:
    RoughChannelProblem(std::shared_ptr<const GridGeometry> gridGeometry)
    : ParentType(gridGeometry)
    {
        name_ = getParam<std::string>("Problem.Name");
        exactWaterDepth_.resize(gridGeometry->numDofs(), 0.0);
        exactVelocityX_.resize(gridGeometry->numDofs(), 0.0);
        constManningN_ = getParam<Scalar>("Problem.ManningN");
        bedSlope_ = getParam<Scalar>("Problem.BedSlope");
        discharge_ = getParam<Scalar>("Problem.Discharge");
        hBoundary_ = this->gauklerManningStrickler(discharge_,constManningN_,bedSlope_);
    }

    const std::vector<Scalar>& getExactWaterDepth()
    {
        return exactWaterDepth_;
    }

    const std::vector<Scalar>& getExactVelocityX()
    {
        return exactVelocityX_;
    }

    Scalar gauklerManningStrickler(Scalar discharge, Scalar manningN, Scalar bedSlope)
    {
        using std::pow;
        using std::abs;
        using std::sqrt;
 
        return pow(abs(discharge)*manningN/sqrt(bedSlope), 0.6);
    }

    void updateAnalyticalSolution()
    {
        using std::abs;
 
        for (const auto& element : elements(this->gridGeometry().gridView()))
        {
            const Scalar h = this->gauklerManningStrickler(discharge_,constManningN_,bedSlope_);
            const Scalar u = abs(discharge_)/h;
 
            const auto eIdx = this->gridGeometry().elementMapper().index(element);
            exactWaterDepth_[eIdx] = h;
            exactVelocityX_[eIdx] = u;
        }
    }

    // \{

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

     NumEqVector source(const Element& element,
                        const FVElementGeometry& fvGeometry,
                        const ElementVolumeVariables& elemVolVars,
                        const SubControlVolume &scv) const
    {
 
        NumEqVector source (0.0);
 
        source += bottomFrictionSource(element, fvGeometry, elemVolVars, scv);
 
        return source;
    }

     NumEqVector bottomFrictionSource(const Element& element,
                                      const FVElementGeometry& fvGeometry,
                                      const ElementVolumeVariables& elemVolVars,
                                      const SubControlVolume &scv) const
     {
        NumEqVector bottomFrictionSource(0.0);
 
        const auto& volVars = elemVolVars[scv];
        Dune::FieldVector<Scalar, 2> bottomShearStress = this->spatialParams().frictionLaw(element, scv).shearStress(volVars);
 
        bottomFrictionSource[0] = 0.0;
        bottomFrictionSource[1] =bottomShearStress[0];
        bottomFrictionSource[2] =bottomShearStress[1];
 
        return bottomFrictionSource;
     }
 
    // \}

    // \{

    BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
    {
        BoundaryTypes bcTypes;
        bcTypes.setAllNeumann();
        return bcTypes;
    }

    NeumannFluxes neumann(const Element& element,
                          const FVElementGeometry& fvGeometry,
                          const ElementVolumeVariables& elemVolVars,
                          const ElementFluxVariablesCache& elemFluxVarsCache,
                          const SubControlVolumeFace& scvf) const
    {
        NeumannFluxes values(0.0);
 
        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
        const auto& insideVolVars = elemVolVars[insideScv];
        const auto& nxy = scvf.unitOuterNormal();
        const auto gravity = this->spatialParams().gravity(scvf.center());
        std::array<Scalar, 3> boundaryStateVariables;
 
        // impose discharge at the left side
        if (scvf.center()[0] < 0.0 + eps_)
        {
            boundaryStateVariables = ShallowWater::fixedDischargeBoundary(discharge_,
                                                                          insideVolVars.waterDepth(),
                                                                          insideVolVars.velocity(0),
                                                                          insideVolVars.velocity(1),
                                                                          gravity,
                                                                          nxy);
        }
        // impose water depth at the right side
        else if (scvf.center()[0] > 100.0 - eps_)
        {
            boundaryStateVariables =  ShallowWater::fixedWaterDepthBoundary(hBoundary_,
                                                                            insideVolVars.waterDepth(),
                                                                            insideVolVars.velocity(0),
                                                                            insideVolVars.velocity(1),
                                                                            gravity,
                                                                            nxy);
        }
        // no flow boundary
        else
        {
            boundaryStateVariables[0] = insideVolVars.waterDepth();
            boundaryStateVariables[1] = -insideVolVars.velocity(0);
            boundaryStateVariables[2] = -insideVolVars.velocity(1);
        }
 
        auto riemannFlux = ShallowWater::riemannProblem(insideVolVars.waterDepth(),
                                                        boundaryStateVariables[0],
                                                        insideVolVars.velocity(0),
                                                        boundaryStateVariables[1],
                                                        insideVolVars.velocity(1),
                                                        boundaryStateVariables[2],
                                                        insideVolVars.bedSurface(),
                                                        insideVolVars.bedSurface(),
                                                        gravity,
                                                        nxy);
 
        values[Indices::massBalanceIdx] = riemannFlux[0];
        values[Indices::velocityXIdx]   = riemannFlux[1];
        values[Indices::velocityYIdx]   = riemannFlux[2];
 
        return values;
    }
 
    // \}

    // \{

    PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const
    {
        PrimaryVariables values(0.0);
 
        values[0] = hBoundary_;
        values[1] = abs(discharge_)/hBoundary_;
        values[2] = 0.0;
 
        return values;
    };
 
    // \}
 
private:
    std::vector<Scalar> exactWaterDepth_;
    std::vector<Scalar> exactVelocityX_;
    Scalar hBoundary_;
    Scalar constManningN_; // analytic solution is only available for const friction.
    Scalar bedSlope_;
    Scalar discharge_; // discharge at the inflow boundary
    static constexpr Scalar eps_ = 1.0e-6;
    std::string name_;
};
 
} //end namespace Dumux
 
#endif