test/geomechanics/elastic/problem.hh

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#ifndef DUMUX_ELASTICPROBLEM_HH
#define DUMUX_ELASTICPROBLEM_HH
 
#include <dune/common/fmatrix.hh>
#include <dune/grid/yaspgrid.hh>
 
#include <dumux/discretization/box.hh>
#include <dumux/geomechanics/elastic/model.hh>
#include <dumux/geomechanics/fvproblem.hh>
 
#include "spatialparams.hh"
 
namespace Dumux {
 
template <class TypeTag>
class ElasticProblem;
 
namespace Properties {
// Create new type tags
namespace TTag {
struct TestElastic { using InheritsFrom = std::tuple<Elastic, BoxModel>; };
} // end namespace TTag
// Set the grid type
template<class TypeTag>
struct Grid<TypeTag, TTag::TestElastic> { using type = Dune::YaspGrid<2>; };
// Set the problem property
template<class TypeTag>
struct Problem<TypeTag, TTag::TestElastic> { using type = Dumux::ElasticProblem<TypeTag>; };
// The spatial parameters property
template<class TypeTag>
struct SpatialParams<TypeTag, TTag::TestElastic>
{ using type = ElasticSpatialParams< GetPropType<TypeTag, Properties::Scalar>,
                                     GetPropType<TypeTag, Properties::GridGeometry> >;
};
} // end namespace Properties
 
template<class TypeTag>
class ElasticProblem : public GeomechanicsFVProblem<TypeTag>
{
    using ParentType = GeomechanicsFVProblem<TypeTag>;
 
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
    using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
    using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;
 
    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
    using ElementVolumeVariables = typename GridVariables::GridVolumeVariables::LocalView;
    using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView;
 
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolume = typename GridGeometry::SubControlVolume;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
 
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using Element = typename GridView::template Codim<0>::Entity;
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
 
    static constexpr Scalar pi = M_PI;
    static constexpr int dim = GridView::dimension;
    static constexpr int dimWorld = GridView::dimensionworld;
    using GradU = Dune::FieldMatrix<Scalar, dim, dimWorld>;
 
public:
    ElasticProblem(std::shared_ptr<const GridGeometry> gridGeometry)
    : ParentType(gridGeometry) {}
 
    static constexpr Scalar temperature()
    { return 273.15; }
 
    PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const
    { return PrimaryVariables(0.0); }
 
    PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
    { return PrimaryVariables(0.0); }
 
    BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
    {
        BoundaryTypes values;
        values.setAllDirichlet();
 
        if (globalPos[0] < eps_ && globalPos[1] > eps_ && globalPos[1] < 1.0 - eps_)
            values.setNeumann(Indices::momentum(/*x-dir*/0));
        if (globalPos[1] > 1.0 - eps_ && globalPos[0] > eps_ && globalPos[0] < 1.0 - eps_)
            values.setNeumann(Indices::momentum(/*y-dir*/1));
 
        return values;
    }
 
    NumEqVector neumann(const Element& element,
                        const FVElementGeometry& fvGeometry,
                        const ElementVolumeVariables& elemVolvars,
                        const ElementFluxVariablesCache& elemFluxVarsCache,
                        const SubControlVolumeFace& scvf) const
    {
        GradU gradU = exactGradient(scvf.ipGlobal());
 
        GradU epsilon;
        for (int i = 0; i < dim; ++i)
            for (int j = 0; j < dimWorld; ++j)
                epsilon[i][j] = 0.5*(gradU[i][j] + gradU[j][i]);
 
        const auto& lameParams = this->spatialParams().lameParamsAtPos(scvf.ipGlobal());
        GradU sigma(0.0);
        const auto traceEpsilon = trace(epsilon);
        for (int i = 0; i < dim; ++i)
        {
            sigma[i][i] = lameParams.lambda()*traceEpsilon;
            for (int j = 0; j < dimWorld; ++j)
                sigma[i][j] += 2.0*lameParams.mu()*epsilon[i][j];
        }
 
        NumEqVector values;
        sigma.mv(scvf.unitOuterNormal(), values);
        return values;
    }
 
    NumEqVector source(const Element& element,
                       const FVElementGeometry& fvGeometry,
                       const ElementVolumeVariables& elemVolVars,
                       const SubControlVolume& scv) const
    {
        using std::sin;
        using std::cos;
 
        const auto ipGlobal = scv.center();
        const auto x = ipGlobal[0];
        const auto y = ipGlobal[1];
 
        // the lame parameters (we know they only depend on the position here)
        const auto& lameParams = this->spatialParams().lameParamsAtPos(scv.center());
        const auto lambda = lameParams.lambda();
        const auto mu = lameParams.mu();
 
        // precalculated products
        const Scalar pi_2 = 2.0*pi;
        const Scalar pi_2_square = pi_2*pi_2;
        const Scalar cos_2pix = cos(pi_2*x);
        const Scalar sin_2pix = sin(pi_2*x);
        const Scalar cos_2piy = cos(pi_2*y);
        const Scalar sin_2piy = sin(pi_2*y);
 
        const Scalar dE11_dx = -2.0*sin_2piy;
        const Scalar dE22_dx = pi_2_square*cos_2pix*cos_2piy;
        const Scalar dE11_dy = pi_2*(1.0-2.0*x)*cos_2piy;
        const Scalar dE22_dy = -1.0*pi_2_square*sin_2pix*sin_2piy;
        const Scalar dE12_dy = 0.5*pi_2_square*(cos_2pix*cos_2piy - (x-x*x)*sin_2piy);
        const Scalar dE21_dx = 0.5*((1.0-2*x)*pi_2*cos_2piy - pi_2_square*sin_2pix*sin_2piy);
 
        // compute exact divergence of sigma
        PrimaryVariables divSigma(0.0);
        divSigma[Indices::momentum(/*x-dir*/0)] = lambda*(dE11_dx + dE22_dx) + 2*mu*(dE11_dx + dE12_dy);
        divSigma[Indices::momentum(/*y-dir*/1)] = lambda*(dE11_dy + dE22_dy) + 2*mu*(dE21_dx + dE22_dy);
        return divSigma;
    }
 
    PrimaryVariables exactSolution(const GlobalPosition& globalPos) const
    {
        using std::sin;
 
        const auto x = globalPos[0];
        const auto y = globalPos[1];
 
        PrimaryVariables exact(0.0);
        exact[Indices::momentum(/*x-dir*/0)] = (x-x*x)*sin(2*pi*y);
        exact[Indices::momentum(/*y-dir*/1)] = sin(2*pi*x)*sin(2*pi*y);
        return exact;
    }
 
    GradU exactGradient(const GlobalPosition& globalPos) const
    {
        using std::sin;
        using std::cos;
 
        const auto x = globalPos[0];
        const auto y = globalPos[1];
 
        static constexpr int xIdx = Indices::momentum(/*x-dir*/0);
        static constexpr int yIdx = Indices::momentum(/*y-dir*/1);
 
        GradU exactGrad(0.0);
        exactGrad[xIdx][xIdx] = (1-2*x)*sin(2*pi*y);
        exactGrad[xIdx][yIdx] = (x - x*x)*2*pi*cos(2*pi*y);
        exactGrad[yIdx][xIdx] = 2*pi*cos(2*pi*x)*sin(2*pi*y);
        exactGrad[yIdx][yIdx] = 2*pi*sin(2*pi*x)*cos(2*pi*y);
        return exactGrad;
    }
 
private:
    static constexpr Scalar eps_ = 3e-6;
};
 
} // end namespace Dumux
 
#endif