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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 | #ifndef DUMUX_EXAMPLES_CAHN_HILLIARD_MODEL_HH | ||
| 9 | #define DUMUX_EXAMPLES_CAHN_HILLIARD_MODEL_HH | ||
| 10 | |||
| 11 | // # Cahn-Hilliard equation model definition | ||
| 12 | // | ||
| 13 | // In the file `model.hh`, we define the model equations and | ||
| 14 | // set all default model properties. The setup consist of four steps: | ||
| 15 | // 1. Create a model type tag (used to specialize properties) | ||
| 16 | // 2. Define the volume variables class computing and storing variables for a control volume | ||
| 17 | // 3. Define the local residual class implementing the discrete equation | ||
| 18 | // 4. Specialize important properties of the model such that Dumux knows how to assemble the system matrix | ||
| 19 | // | ||
| 20 | // We implement the classes | ||
| 21 | // | ||
| 22 | // * `CahnHilliardModel` (step 1), | ||
| 23 | // * `CahnHilliardModelVolumeVariables` (step 2) and | ||
| 24 | // * `CahnHilliardModelLocalResidual` (step 3). | ||
| 25 | // | ||
| 26 | // __Table of contents__ | ||
| 27 | // | ||
| 28 | // [TOC] | ||
| 29 | // | ||
| 30 | // We start in `model.hh` with the necessary header includes: | ||
| 31 | // [[details]] includes | ||
| 32 | #include <dune/common/fvector.hh> | ||
| 33 | #include <dumux/common/math.hh> | ||
| 34 | #include <dumux/common/properties.hh> | ||
| 35 | #include <dumux/common/numeqvector.hh> | ||
| 36 | #include <dumux/discretization/method.hh> | ||
| 37 | // [[/details]] | ||
| 38 | // | ||
| 39 | // ## 1. Property Tag | ||
| 40 | // | ||
| 41 | // The property tag is simply an empty struct with the name `CahnHilliardModel`. | ||
| 42 | // | ||
| 43 | // [[content]] | ||
| 44 | // [[codeblock]] | ||
| 45 | namespace Dumux::Properties::TTag { | ||
| 46 | struct CahnHilliardModel {}; | ||
| 47 | } // end namespace Dumux::Properties::TTag | ||
| 48 | // [[/codeblock]] | ||
| 49 | // [[/content]] | ||
| 50 | // | ||
| 51 | // ## 2. The volume variables | ||
| 52 | // | ||
| 53 | // The volume variables store the control volume variables, both primary and secondary. | ||
| 54 | // Let's have a look at the class implementation. | ||
| 55 | // | ||
| 56 | // [[content]] | ||
| 57 | // | ||
| 58 | // We write out a full volume variable class compatible with the Dumux assembly. | ||
| 59 | // We have to fulfill the same interface as the [`BasicVolumeVariables`](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/dumux/common/volumevariables.hh). | ||
| 60 | // To shorten the code, we could also inherit from `BasicVolumeVariables`. However, | ||
| 61 | // we want to show the entire interface here as a basis for the implementation of more complex variables. | ||
| 62 | // Note that in `update` we could, for example, compute some secondary variable that is a | ||
| 63 | // possibly nonlinear function of the primary variables. That secondary variable could be exposed | ||
| 64 | // via an interface and then used below in the `CahnHilliardModelLocalResidual` class implementation. | ||
| 65 | // | ||
| 66 | // [[codeblock]] | ||
| 67 | namespace Dumux { | ||
| 68 | template <class Traits> | ||
| 69 | 1920 | class CahnHilliardModelVolumeVariables | |
| 70 | { | ||
| 71 | using Scalar = typename Traits::PrimaryVariables::value_type; | ||
| 72 | static_assert(Traits::PrimaryVariables::dimension == Traits::ModelTraits::numEq()); | ||
| 73 | public: | ||
| 74 | //! export the type used for the primary variables | ||
| 75 | using PrimaryVariables = typename Traits::PrimaryVariables; | ||
| 76 | //! export the indices type | ||
| 77 | using Indices = typename Traits::ModelTraits::Indices; | ||
| 78 | // [[/codeblock]] | ||
| 79 | // | ||
| 80 | // **Update variables:** The `update` function stores the local primary variables of the current solution and | ||
| 81 | // potentially computes secondary variables. Secondary variables can be nonlinear functions | ||
| 82 | // of the primary variables. | ||
| 83 | // | ||
| 84 | // [[codeblock]] | ||
| 85 | //! Update all quantities for a given control volume | ||
| 86 | template<class ElementSolution, class Problem, class Element, class SubControlVolume> | ||
| 87 | ✗ | void update(const ElementSolution& elemSol, | |
| 88 | const Problem& problem, | ||
| 89 | const Element& element, | ||
| 90 | const SubControlVolume& scv) | ||
| 91 | { | ||
| 92 | 2460160 | priVars_ = elemSol[scv.indexInElement()]; | |
| 93 | ✗ | } | |
| 94 | // [[/codeblock]] | ||
| 95 | // | ||
| 96 | // **Access functions:** Named and generic functions to access different primary variables. | ||
| 97 | // The volumevariables are also expected to return an extrusion factor. | ||
| 98 | // Here we don't extrude our domain and therefore return $1.0$. | ||
| 99 | // [[codeblock]] | ||
| 100 | Scalar concentration() const | ||
| 101 | 51584000 | { return priVars_[Indices::concentrationIdx]; } | |
| 102 | |||
| 103 | Scalar chemicalPotential() const | ||
| 104 | 36892800 | { return priVars_[Indices::chemicalPotentialIdx]; } | |
| 105 | |||
| 106 | Scalar priVar(const int pvIdx) const | ||
| 107 | { return priVars_[pvIdx]; } | ||
| 108 | |||
| 109 | const PrimaryVariables& priVars() const | ||
| 110 | ✗ | { return priVars_; } | |
| 111 | |||
| 112 | ✗ | Scalar extrusionFactor() const | |
| 113 | ✗ | { return 1.0; } | |
| 114 | |||
| 115 | private: | ||
| 116 | PrimaryVariables priVars_; | ||
| 117 | }; | ||
| 118 | } // end namespace Dumux | ||
| 119 | // [[/codeblock]] | ||
| 120 | // [[/content]] | ||
| 121 | // | ||
| 122 | // ## 3. The local residual | ||
| 123 | // | ||
| 124 | // The local residual assembles the contribution to the residual for | ||
| 125 | // all degrees of freedom associated with an element. | ||
| 126 | // See [examples/diffusion/doc/model.hh](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/examples/diffusion/doc/main.md) | ||
| 127 | // for a more detailed explanation for control-volume finite element method local residuals. | ||
| 128 | // Let's have a look at the class implementation. | ||
| 129 | // | ||
| 130 | // [[content]] | ||
| 131 | // | ||
| 132 | // The class `CahnHilliardModelLocalResidual` inherits from a base class set in | ||
| 133 | // the model properties, depending on the discretization scheme. | ||
| 134 | // See [examples/diffusion/doc/model.hh](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/examples/diffusion/doc/main.md) | ||
| 135 | // for details on the `BaseLocalResidual`. | ||
| 136 | namespace Dumux { | ||
| 137 | template<class TypeTag> | ||
| 138 | class CahnHilliardModelLocalResidual | ||
| 139 | : public GetPropType<TypeTag, Properties::BaseLocalResidual> | ||
| 140 | { | ||
| 141 | // [[exclude]] | ||
| 142 | // the base local residual is selected depending on the chosen discretization scheme | ||
| 143 | using ParentType = GetPropType<TypeTag, Properties::BaseLocalResidual>; | ||
| 144 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 145 | using Problem = GetPropType<TypeTag, Properties::Problem>; | ||
| 146 | using NumEqVector = Dumux::NumEqVector<GetPropType<TypeTag, Properties::PrimaryVariables>>; | ||
| 147 | |||
| 148 | using GridVariables = GetPropType<TypeTag, Properties::GridVariables>; | ||
| 149 | using VolumeVariables = typename GridVariables::GridVolumeVariables::VolumeVariables; | ||
| 150 | using ElementVolumeVariables = typename GridVariables::GridVolumeVariables::LocalView; | ||
| 151 | using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView; | ||
| 152 | |||
| 153 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 154 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 155 | using SubControlVolume = typename GridGeometry::SubControlVolume; | ||
| 156 | using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; | ||
| 157 | using GridView = typename GridGeometry::GridView; | ||
| 158 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 159 | |||
| 160 | using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>; | ||
| 161 | using Indices = typename ModelTraits::Indices; | ||
| 162 | static constexpr int dimWorld = GridView::dimensionworld; | ||
| 163 | public: | ||
| 164 | 207280 | using ParentType::ParentType; | |
| 165 | // [[/exclude]] | ||
| 166 | // | ||
| 167 | // **Storage term:** The function `computeStorage` receives the volume variables | ||
| 168 | // at the previous or current time step and computes the value of the storage terms. | ||
| 169 | // In this case the mass balance equation is a conservation equation of the concentration and | ||
| 170 | // the equation for the chemical potential does not have a storage term. | ||
| 171 | // | ||
| 172 | // [[codeblock]] | ||
| 173 | ✗ | NumEqVector computeStorage(const Problem& problem, | |
| 174 | const SubControlVolume& scv, | ||
| 175 | const VolumeVariables& volVars) const | ||
| 176 | { | ||
| 177 | 7345600 | NumEqVector storage; | |
| 178 | 14691200 | storage[Indices::massBalanceEqIdx] = volVars.concentration(); | |
| 179 | 14691200 | storage[Indices::chemicalPotentialEqIdx] = 0.0; | |
| 180 | ✗ | return storage; | |
| 181 | } | ||
| 182 | // [[/codeblock]] | ||
| 183 | |||
| 184 | // **Flux term:** The function `computeFlux` computes the integrated | ||
| 185 | // fluxes over a sub control volume face. | ||
| 186 | // | ||
| 187 | // ```math | ||
| 188 | // \begin{aligned} | ||
| 189 | // F_{K,\sigma,0} &= -M \vert \sigma \vert \sum_{B \in \mathcal{B}_K} \mu_{h,B} \nabla N_B \cdot\boldsymbol{n} \cr | ||
| 190 | // F_{K,\sigma,1} &= -\gamma \vert \sigma \vert \sum_{B \in \mathcal{B}_K} c_{h,B} \nabla N_B \cdot\boldsymbol{n} | ||
| 191 | // \end{aligned} | ||
| 192 | // ```` | ||
| 193 | // | ||
| 194 | // [[codeblock]] | ||
| 195 | 3672800 | NumEqVector computeFlux(const Problem& problem, | |
| 196 | const Element& element, | ||
| 197 | const FVElementGeometry& fvGeometry, | ||
| 198 | const ElementVolumeVariables& elemVolVars, | ||
| 199 | const SubControlVolumeFace& scvf, | ||
| 200 | const ElementFluxVariablesCache& elemFluxVarsCache) const | ||
| 201 | { | ||
| 202 | static_assert(DiscretizationMethods::isCVFE<typename GridGeometry::DiscretizationMethod>, | ||
| 203 | "This local residual is hard-coded to control-volume finite element schemes"); | ||
| 204 | |||
| 205 | 3672800 | const auto& fluxVarCache = elemFluxVarsCache[scvf]; | |
| 206 | 3672800 | Dune::FieldVector<Scalar, dimWorld> gradConcentration(0.0); | |
| 207 | 3672800 | Dune::FieldVector<Scalar, dimWorld> gradChemicalPotential(0.0); | |
| 208 |
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36728000 | for (const auto& scv : scvs(fvGeometry)) |
| 209 | { | ||
| 210 | 14691200 | const auto& volVars = elemVolVars[scv]; | |
| 211 | // v.axpy(a, w) means v += a*w | ||
| 212 | 44073600 | gradConcentration.axpy( | |
| 213 | volVars.concentration(), | ||
| 214 | fluxVarCache.gradN(scv.indexInElement()) | ||
| 215 | ); | ||
| 216 | 58764800 | gradChemicalPotential.axpy( | |
| 217 | volVars.chemicalPotential(), | ||
| 218 | fluxVarCache.gradN(scv.indexInElement()) | ||
| 219 | ); | ||
| 220 | } | ||
| 221 | |||
| 222 | 3672800 | NumEqVector flux; | |
| 223 | // Compute the flux with `vtmv` (vector transposed times matrix times vector). | ||
| 224 | // The mobility and surface tension coefficients comes from the `problem` (see Part 2 of the example). | ||
| 225 | 7345600 | flux[Indices::massBalanceEqIdx] = -1.0*vtmv( | |
| 226 | scvf.unitOuterNormal(), problem.mobility(), gradChemicalPotential | ||
| 227 | 3672800 | )*scvf.area(); | |
| 228 | 7345600 | flux[Indices::chemicalPotentialEqIdx] = -1.0*vtmv( | |
| 229 | scvf.unitOuterNormal(), problem.surfaceTension(), gradConcentration | ||
| 230 | 3672800 | )*scvf.area(); | |
| 231 | 3672800 | return flux; | |
| 232 | } | ||
| 233 | // [[/codeblock]] | ||
| 234 | |||
| 235 | // **Source term:** The function `computeSource` computes the source terms for a sub control volume. | ||
| 236 | // We implement a model-specific source term for the chemical potential equation before | ||
| 237 | // deferring further implementation to the problem where we add the derivative of the free | ||
| 238 | // energy. | ||
| 239 | // | ||
| 240 | // [[codeblock]] | ||
| 241 | 3672800 | NumEqVector computeSource(const Problem& problem, | |
| 242 | const Element& element, | ||
| 243 | const FVElementGeometry& fvGeometry, | ||
| 244 | const ElementVolumeVariables& elemVolVars, | ||
| 245 | const SubControlVolume &scv) const | ||
| 246 | { | ||
| 247 | 3672800 | NumEqVector source(0.0); | |
| 248 | 3672800 | source[Indices::massBalanceEqIdx] = 0.0; | |
| 249 | 11018400 | source[Indices::chemicalPotentialEqIdx] = elemVolVars[scv].chemicalPotential(); | |
| 250 | // add contributions from problem (e.g. double well potential) | ||
| 251 | 3672800 | source += problem.source(element, fvGeometry, elemVolVars, scv); | |
| 252 | 3672800 | return source; | |
| 253 | } | ||
| 254 | }; | ||
| 255 | } // end namespace Dumux | ||
| 256 | // [[/codeblock]] | ||
| 257 | // [[/content]] | ||
| 258 | // | ||
| 259 | // ## 4. The model properties/traits | ||
| 260 | // | ||
| 261 | // In the `Dumux::Properties` namespace, we specialize properties for | ||
| 262 | // the created type tag `CahnHilliardModel`. | ||
| 263 | // | ||
| 264 | // [[content]] | ||
| 265 | namespace Dumux::Properties { | ||
| 266 | |||
| 267 | // The type of the local residual is the class defined above. | ||
| 268 | template<class TypeTag> | ||
| 269 | struct LocalResidual<TypeTag, TTag::CahnHilliardModel> | ||
| 270 | { using type = CahnHilliardModelLocalResidual<TypeTag>; }; | ||
| 271 | |||
| 272 | // We compute with double precision floating point numbers. | ||
| 273 | template<class TypeTag> | ||
| 274 | struct Scalar<TypeTag, TTag::CahnHilliardModel> | ||
| 275 | { using type = double; }; | ||
| 276 | |||
| 277 | // The model traits specify some information about our equation system. | ||
| 278 | // Here we have two equations. The indices allow to access primary variables | ||
| 279 | // and equations with named indices. | ||
| 280 | template<class TypeTag> | ||
| 281 | struct ModelTraits<TypeTag, TTag::CahnHilliardModel> | ||
| 282 | { | ||
| 283 | struct type | ||
| 284 | { | ||
| 285 | struct Indices | ||
| 286 | { | ||
| 287 | static constexpr int concentrationIdx = 0; | ||
| 288 | static constexpr int chemicalPotentialIdx = 1; | ||
| 289 | |||
| 290 | static constexpr int massBalanceEqIdx = 0; | ||
| 291 | static constexpr int chemicalPotentialEqIdx = 1; | ||
| 292 | }; | ||
| 293 | |||
| 294 | static constexpr int numEq() { return 2; } | ||
| 295 | }; | ||
| 296 | }; | ||
| 297 | |||
| 298 | // The primary variable vector has entries of type `Scalar` and is | ||
| 299 | // as large as the number of equations (here 2) but we keep it general | ||
| 300 | // here by obtaining the number of equations from the `ModelTraits`. | ||
| 301 | template<class TypeTag> | ||
| 302 | struct PrimaryVariables<TypeTag, TTag::CahnHilliardModel> | ||
| 303 | { | ||
| 304 | using type = Dune::FieldVector< | ||
| 305 | GetPropType<TypeTag, Properties::Scalar>, | ||
| 306 | GetPropType<TypeTag, Properties::ModelTraits>::numEq() | ||
| 307 | >; | ||
| 308 | }; | ||
| 309 | |||
| 310 | // Finally, the type of the volume variables is the class defined above. | ||
| 311 | template<class TypeTag> | ||
| 312 | struct VolumeVariables<TypeTag, TTag::CahnHilliardModel> | ||
| 313 | { | ||
| 314 | struct Traits | ||
| 315 | { | ||
| 316 | using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; | ||
| 317 | using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>; | ||
| 318 | }; | ||
| 319 | |||
| 320 | using type = CahnHilliardModelVolumeVariables<Traits>; | ||
| 321 | }; | ||
| 322 | |||
| 323 | } // end namespace Dumux::Properties | ||
| 324 | // [[/content]] | ||
| 325 | // [[exclude]] | ||
| 326 | #endif | ||
| 327 | // [[/exclude]] | ||
| 328 |