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| 1 | // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- | ||
| 2 | // vi: set et ts=4 sw=4 sts=4: | ||
| 3 | // | ||
| 4 | // SPDX-FileCopyrightText: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | /*! | ||
| 8 | * \file | ||
| 9 | * \ingroup GeomechanicsTests | ||
| 10 | * \brief Definition of a test problem for the linear elastic model. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_ELASTICPROBLEM_HH | ||
| 13 | #define DUMUX_ELASTICPROBLEM_HH | ||
| 14 | |||
| 15 | #include <dune/common/fmatrix.hh> | ||
| 16 | |||
| 17 | #include <dumux/common/math.hh> | ||
| 18 | #include <dumux/common/properties.hh> | ||
| 19 | #include <dumux/common/parameters.hh> | ||
| 20 | #include <dumux/common/boundarytypes.hh> | ||
| 21 | #include <dumux/common/numeqvector.hh> | ||
| 22 | #include <dumux/common/fvproblemwithspatialparams.hh> | ||
| 23 | |||
| 24 | namespace Dumux { | ||
| 25 | |||
| 26 | /*! | ||
| 27 | * \ingroup GeomechanicsTests | ||
| 28 | * \brief Problem definition for the deformation of an elastic body. | ||
| 29 | */ | ||
| 30 | template<class TypeTag> | ||
| 31 | 1 | class ElasticProblem : public FVProblemWithSpatialParams<TypeTag> | |
| 32 | { | ||
| 33 | using ParentType = FVProblemWithSpatialParams<TypeTag>; | ||
| 34 | |||
| 35 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 36 | using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices; | ||
| 37 | using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>; | ||
| 38 | using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; | ||
| 39 | using NumEqVector = Dumux::NumEqVector<PrimaryVariables>; | ||
| 40 | |||
| 41 | using GridVariables = GetPropType<TypeTag, Properties::GridVariables>; | ||
| 42 | using ElementVolumeVariables = typename GridVariables::GridVolumeVariables::LocalView; | ||
| 43 | using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView; | ||
| 44 | |||
| 45 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 46 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 47 | using SubControlVolume = typename GridGeometry::SubControlVolume; | ||
| 48 | using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; | ||
| 49 | |||
| 50 | using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView; | ||
| 51 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 52 | using GlobalPosition = typename Element::Geometry::GlobalCoordinate; | ||
| 53 | |||
| 54 | static constexpr Scalar pi = M_PI; | ||
| 55 | static constexpr int dim = GridView::dimension; | ||
| 56 | static constexpr int dimWorld = GridView::dimensionworld; | ||
| 57 | using GradU = Dune::FieldMatrix<Scalar, dim, dimWorld>; | ||
| 58 | |||
| 59 | public: | ||
| 60 | 1 | ElasticProblem(std::shared_ptr<const GridGeometry> gridGeometry) | |
| 61 |
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3 | : ParentType(gridGeometry) {} |
| 62 | |||
| 63 | //! Evaluates the initial value for a control volume. | ||
| 64 | 121 | PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const | |
| 65 | 242 | { return PrimaryVariables(0.0); } | |
| 66 | |||
| 67 | //! Evaluates the boundary conditions for a Dirichlet boundary segment. | ||
| 68 | 152 | PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const | |
| 69 | 304 | { return PrimaryVariables(0.0); } | |
| 70 | |||
| 71 | /*! | ||
| 72 | * \brief Specifies which kind of boundary condition should be | ||
| 73 | * used for which equation on a given boundary segment. | ||
| 74 | * | ||
| 75 | * \param globalPos The global position | ||
| 76 | */ | ||
| 77 | 152 | BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const | |
| 78 | { | ||
| 79 |
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456 | BoundaryTypes values; |
| 80 |
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152 | values.setAllDirichlet(); |
| 81 | |||
| 82 |
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152 | if (globalPos[0] < eps_ && globalPos[1] > eps_ && globalPos[1] < 1.0 - eps_) |
| 83 | 36 | values.setNeumann(Indices::momentum(/*x-dir*/0)); | |
| 84 |
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152 | if (globalPos[1] > 1.0 - eps_ && globalPos[0] > eps_ && globalPos[0] < 1.0 - eps_) |
| 85 | 36 | values.setNeumann(Indices::momentum(/*y-dir*/1)); | |
| 86 | |||
| 87 | 152 | return values; | |
| 88 | } | ||
| 89 | |||
| 90 | //! Evaluates the boundary conditions for a Neumann boundary segment. | ||
| 91 | 648 | NumEqVector neumann(const Element& element, | |
| 92 | const FVElementGeometry& fvGeometry, | ||
| 93 | const ElementVolumeVariables& elemVolvars, | ||
| 94 | const ElementFluxVariablesCache& elemFluxVarsCache, | ||
| 95 | const SubControlVolumeFace& scvf) const | ||
| 96 | { | ||
| 97 | 648 | GradU gradU = exactGradient(scvf.ipGlobal()); | |
| 98 | |||
| 99 | 648 | GradU epsilon; | |
| 100 |
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1944 | for (int i = 0; i < dim; ++i) |
| 101 |
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3888 | for (int j = 0; j < dimWorld; ++j) |
| 102 | 2592 | epsilon[i][j] = 0.5*(gradU[i][j] + gradU[j][i]); | |
| 103 | |||
| 104 | 648 | const auto& lameParams = this->spatialParams().lameParamsAtPos(scvf.ipGlobal()); | |
| 105 |
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2592 | GradU sigma(0.0); |
| 106 | 1944 | const auto traceEpsilon = trace(epsilon); | |
| 107 |
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1944 | for (int i = 0; i < dim; ++i) |
| 108 | { | ||
| 109 | 1296 | sigma[i][i] = lameParams.lambda()*traceEpsilon; | |
| 110 |
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3888 | for (int j = 0; j < dimWorld; ++j) |
| 111 | 2592 | sigma[i][j] += 2.0*lameParams.mu()*epsilon[i][j]; | |
| 112 | } | ||
| 113 | |||
| 114 | 648 | NumEqVector values; | |
| 115 | 648 | sigma.mv(scvf.unitOuterNormal(), values); | |
| 116 | 648 | return values; | |
| 117 | } | ||
| 118 | |||
| 119 | /*! | ||
| 120 | * \brief Evaluates the source term for all phases within a given | ||
| 121 | * sub-control volume. | ||
| 122 | */ | ||
| 123 | 7200 | NumEqVector source(const Element& element, | |
| 124 | const FVElementGeometry& fvGeometry, | ||
| 125 | const ElementVolumeVariables& elemVolVars, | ||
| 126 | const SubControlVolume& scv) const | ||
| 127 | { | ||
| 128 | using std::sin; | ||
| 129 | using std::cos; | ||
| 130 | |||
| 131 | 7200 | const auto ipGlobal = scv.center(); | |
| 132 | 7200 | const auto x = ipGlobal[0]; | |
| 133 | 7200 | const auto y = ipGlobal[1]; | |
| 134 | |||
| 135 | // the lame parameters (we know they only depend on the position here) | ||
| 136 | 7200 | const auto& lameParams = this->spatialParams().lameParamsAtPos(scv.center()); | |
| 137 | 7200 | const auto lambda = lameParams.lambda(); | |
| 138 | 7200 | const auto mu = lameParams.mu(); | |
| 139 | |||
| 140 | // precalculated products | ||
| 141 | 7200 | const Scalar pi_2 = 2.0*pi; | |
| 142 | 7200 | const Scalar pi_2_square = pi_2*pi_2; | |
| 143 | 7200 | const Scalar cos_2pix = cos(pi_2*x); | |
| 144 | 7200 | const Scalar sin_2pix = sin(pi_2*x); | |
| 145 | 7200 | const Scalar cos_2piy = cos(pi_2*y); | |
| 146 | 7200 | const Scalar sin_2piy = sin(pi_2*y); | |
| 147 | |||
| 148 | 7200 | const Scalar dE11_dx = -2.0*sin_2piy; | |
| 149 | 7200 | const Scalar dE22_dx = pi_2_square*cos_2pix*cos_2piy; | |
| 150 | 7200 | const Scalar dE11_dy = pi_2*(1.0-2.0*x)*cos_2piy; | |
| 151 | 7200 | const Scalar dE22_dy = -1.0*pi_2_square*sin_2pix*sin_2piy; | |
| 152 | 7200 | const Scalar dE12_dy = 0.5*pi_2_square*(cos_2pix*cos_2piy - (x-x*x)*sin_2piy); | |
| 153 | 7200 | const Scalar dE21_dx = 0.5*((1.0-2*x)*pi_2*cos_2piy - pi_2_square*sin_2pix*sin_2piy); | |
| 154 | |||
| 155 | // compute exact divergence of sigma | ||
| 156 | 7200 | PrimaryVariables divSigma(0.0); | |
| 157 | 7200 | divSigma[Indices::momentum(/*x-dir*/0)] = lambda*(dE11_dx + dE22_dx) + 2*mu*(dE11_dx + dE12_dy); | |
| 158 | 7200 | divSigma[Indices::momentum(/*y-dir*/1)] = lambda*(dE11_dy + dE22_dy) + 2*mu*(dE21_dx + dE22_dy); | |
| 159 | 7200 | return divSigma; | |
| 160 | } | ||
| 161 | |||
| 162 | /*! | ||
| 163 | * \brief Evaluates the exact displacement to this problem at a given position. | ||
| 164 | */ | ||
| 165 | 121 | PrimaryVariables exactSolution(const GlobalPosition& globalPos) const | |
| 166 | { | ||
| 167 | using std::sin; | ||
| 168 | |||
| 169 | 121 | const auto x = globalPos[0]; | |
| 170 | 121 | const auto y = globalPos[1]; | |
| 171 | |||
| 172 | 121 | PrimaryVariables exact(0.0); | |
| 173 | 121 | exact[Indices::momentum(/*x-dir*/0)] = (x-x*x)*sin(2*pi*y); | |
| 174 | 121 | exact[Indices::momentum(/*y-dir*/1)] = sin(2*pi*x)*sin(2*pi*y); | |
| 175 | 121 | return exact; | |
| 176 | } | ||
| 177 | |||
| 178 | /*! | ||
| 179 | * \brief Evaluates the exact displacement gradient to this problem at a given position. | ||
| 180 | */ | ||
| 181 | 648 | GradU exactGradient(const GlobalPosition& globalPos) const | |
| 182 | { | ||
| 183 | using std::sin; | ||
| 184 | using std::cos; | ||
| 185 | |||
| 186 | 648 | const auto x = globalPos[0]; | |
| 187 | 648 | const auto y = globalPos[1]; | |
| 188 | |||
| 189 | static constexpr int xIdx = Indices::momentum(/*x-dir*/0); | ||
| 190 | static constexpr int yIdx = Indices::momentum(/*y-dir*/1); | ||
| 191 | |||
| 192 | 648 | GradU exactGrad(0.0); | |
| 193 | 648 | exactGrad[xIdx][xIdx] = (1-2*x)*sin(2*pi*y); | |
| 194 | 648 | exactGrad[xIdx][yIdx] = (x - x*x)*2*pi*cos(2*pi*y); | |
| 195 | 648 | exactGrad[yIdx][xIdx] = 2*pi*cos(2*pi*x)*sin(2*pi*y); | |
| 196 | 648 | exactGrad[yIdx][yIdx] = 2*pi*sin(2*pi*x)*cos(2*pi*y); | |
| 197 | 648 | return exactGrad; | |
| 198 | } | ||
| 199 | |||
| 200 | private: | ||
| 201 | static constexpr Scalar eps_ = 3e-6; | ||
| 202 | }; | ||
| 203 | |||
| 204 | } // end namespace Dumux | ||
| 205 | |||
| 206 | #endif | ||
| 207 |