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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-FileCopyrightInfo: 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 poro-elastic model. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_POROELASTIC_PROBLEM_HH | ||
| 13 | #define DUMUX_POROELASTIC_PROBLEM_HH | ||
| 14 | |||
| 15 | #include <dune/common/fmatrix.hh> | ||
| 16 | #include <dumux/common/boundarytypes.hh> | ||
| 17 | #include <dumux/common/numeqvector.hh> | ||
| 18 | #include <dumux/geomechanics/fvproblem.hh> | ||
| 19 | |||
| 20 | namespace Dumux { | ||
| 21 | |||
| 22 | /*! | ||
| 23 | * \ingroup GeomechanicsTests | ||
| 24 | * \brief Problem definition for the deformation of a poro-elastic body. | ||
| 25 | */ | ||
| 26 | template<class TypeTag> | ||
| 27 | 3 | class PoroElasticProblem : public GeomechanicsFVProblem<TypeTag> | |
| 28 | { | ||
| 29 | using ParentType = GeomechanicsFVProblem<TypeTag>; | ||
| 30 | |||
| 31 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 32 | using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices; | ||
| 33 | using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>; | ||
| 34 | using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; | ||
| 35 | using NumEqVector = Dumux::NumEqVector<PrimaryVariables>; | ||
| 36 | using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView; | ||
| 37 | |||
| 38 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 39 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 40 | using SubControlVolume = typename GridGeometry::SubControlVolume; | ||
| 41 | using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; | ||
| 42 | |||
| 43 | using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView; | ||
| 44 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 45 | using GlobalPosition = typename Element::Geometry::GlobalCoordinate; | ||
| 46 | |||
| 47 | static constexpr Scalar pi = M_PI; | ||
| 48 | |||
| 49 | public: | ||
| 50 | 1 | PoroElasticProblem(std::shared_ptr<const GridGeometry> gridGeometry) | |
| 51 |
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3 | : ParentType(gridGeometry) |
| 52 | 1 | {} | |
| 53 | |||
| 54 | //! Evaluates the initial value for a control volume. | ||
| 55 | ✗ | PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const | |
| 56 | ✗ | { return PrimaryVariables(0.0); } | |
| 57 | |||
| 58 | //! Evaluates the boundary conditions for a Dirichlet boundary segment. | ||
| 59 | ✗ | PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const | |
| 60 | 304 | { return PrimaryVariables(0.0); } | |
| 61 | |||
| 62 | /*! | ||
| 63 | * \brief Specifies which kind of boundary condition should be | ||
| 64 | * used for which equation on a given boundary segment. | ||
| 65 | * | ||
| 66 | * \param globalPos The global position | ||
| 67 | */ | ||
| 68 | ✗ | BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const | |
| 69 | { | ||
| 70 | 152 | BoundaryTypes values; | |
| 71 |
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152 | values.setAllDirichlet(); |
| 72 | ✗ | return values; | |
| 73 | } | ||
| 74 | |||
| 75 | /*! | ||
| 76 | * \brief Evaluates the source term for all phases within a given | ||
| 77 | * sub-control volume. | ||
| 78 | */ | ||
| 79 | 7200 | NumEqVector source(const Element& element, | |
| 80 | const FVElementGeometry& fvGeometry, | ||
| 81 | const ElementVolumeVariables& elemVolVars, | ||
| 82 | const SubControlVolume& scv) const | ||
| 83 | { | ||
| 84 | using std::sin; | ||
| 85 | using std::cos; | ||
| 86 | |||
| 87 | 7200 | const auto ipGlobal = scv.center(); | |
| 88 | 7200 | const auto x = ipGlobal[0]; | |
| 89 | 7200 | const auto y = ipGlobal[1]; | |
| 90 | |||
| 91 | // the lame parameters (we know they only depend on position here) | ||
| 92 | 21600 | const auto& lameParams = this->spatialParams().lameParamsAtPos(scv.center()); | |
| 93 | 7200 | const auto lambda = lameParams.lambda(); | |
| 94 | 7200 | const auto mu = lameParams.mu(); | |
| 95 | |||
| 96 | // precalculated products | ||
| 97 | 7200 | const Scalar pi_2 = 2.0*pi; | |
| 98 | 7200 | const Scalar pi_2_square = pi_2*pi_2; | |
| 99 | 7200 | const Scalar cos_2pix = cos(pi_2*x); | |
| 100 | 7200 | const Scalar sin_2pix = sin(pi_2*x); | |
| 101 | 7200 | const Scalar cos_2piy = cos(pi_2*y); | |
| 102 | 7200 | const Scalar sin_2piy = sin(pi_2*y); | |
| 103 | |||
| 104 | 7200 | const Scalar dE11_dx = -2.0*sin_2piy; | |
| 105 | 7200 | const Scalar dE22_dx = pi_2_square*cos_2pix*cos_2piy; | |
| 106 | 7200 | const Scalar dE11_dy = pi_2*(1.0-2.0*x)*cos_2piy; | |
| 107 | 7200 | const Scalar dE22_dy = -1.0*pi_2_square*sin_2pix*sin_2piy; | |
| 108 | 7200 | const Scalar dE12_dy = 0.5*pi_2_square*(cos_2pix*cos_2piy - (x-x*x)*sin_2piy); | |
| 109 | 7200 | const Scalar dE21_dx = 0.5*((1.0-2*x)*pi_2*cos_2piy - pi_2_square*sin_2pix*sin_2piy); | |
| 110 | |||
| 111 | // The source term is composed of the divergence of the stress tensor | ||
| 112 | // resulting from the exact solution minus the pressure gradient | ||
| 113 | 7200 | PrimaryVariables divSigma(0.0); | |
| 114 | 7200 | divSigma[Indices::momentum(/*x-dir*/0)] = lambda*(dE11_dx + dE22_dx) + 2*mu*(dE11_dx + dE12_dy); | |
| 115 | 7200 | divSigma[Indices::momentum(/*y-dir*/1)] = lambda*(dE11_dy + dE22_dy) + 2*mu*(dE21_dx + dE22_dy); | |
| 116 | 14400 | divSigma -= this->spatialParams().effectivePorePressureGradient(ipGlobal); | |
| 117 | 7200 | return divSigma; | |
| 118 | } | ||
| 119 | |||
| 120 | /*! | ||
| 121 | * \brief Evaluates the exact displacement to this problem at a given position. | ||
| 122 | */ | ||
| 123 | 121 | PrimaryVariables exactDisplacement(const GlobalPosition& globalPos) const | |
| 124 | { | ||
| 125 | using std::sin; | ||
| 126 | |||
| 127 | 121 | const auto x = globalPos[0]; | |
| 128 | 121 | const auto y = globalPos[1]; | |
| 129 | |||
| 130 | 121 | PrimaryVariables exact(0.0); | |
| 131 | 242 | exact[Indices::momentum(/*x-dir*/0)] = (x-x*x)*sin(2*pi*y); | |
| 132 | 242 | exact[Indices::momentum(/*y-dir*/1)] = sin(2*pi*x)*sin(2*pi*y); | |
| 133 | 121 | return exact; | |
| 134 | } | ||
| 135 | |||
| 136 | private: | ||
| 137 | static constexpr Scalar eps_ = 3e-6; | ||
| 138 | }; | ||
| 139 | |||
| 140 | } // end namespace Dumux | ||
| 141 | |||
| 142 | #endif | ||
| 143 |