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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 | #ifndef DUMUX_EXAMPLES_DIFFUSION_MODEL_HH | ||
| 9 | #define DUMUX_EXAMPLES_DIFFUSION_MODEL_HH | ||
| 10 | |||
| 11 | // In the file `model.hh`, we define the model equations and | ||
| 12 | // set all default model properties. The setup consist of three steps: | ||
| 13 | // 1. Create a model type tag (used to specialize properties) | ||
| 14 | // 2. Define the local residual class implementing the discrete equation | ||
| 15 | // 3. Specialize important properties of the model such that Dumux knows how to assemble the system matrix | ||
| 16 | // | ||
| 17 | // __Table of contents__ | ||
| 18 | // | ||
| 19 | // [TOC] | ||
| 20 | // | ||
| 21 | // We start in `model.hh` with the necessary header includes: | ||
| 22 | // [[details]] includes | ||
| 23 | #include <dune/common/fvector.hh> | ||
| 24 | #include <dumux/common/math.hh> | ||
| 25 | #include <dumux/common/properties.hh> | ||
| 26 | #include <dumux/common/numeqvector.hh> | ||
| 27 | #include <dumux/common/volumevariables.hh> | ||
| 28 | #include <dumux/discretization/method.hh> | ||
| 29 | #include <dumux/discretization/defaultlocaloperator.hh> | ||
| 30 | // [[/details]] | ||
| 31 | // | ||
| 32 | // ## 1. Property Tag | ||
| 33 | // | ||
| 34 | // The property tag is simply an empty struct with the name `DiffusionModel` | ||
| 35 | // | ||
| 36 | // [[content]] | ||
| 37 | // [[codeblock]] | ||
| 38 | namespace Dumux::Properties::TTag { | ||
| 39 | //! The diffusion model tag that we can specialize properties for | ||
| 40 | struct DiffusionModel {}; | ||
| 41 | } // end namespace Dumux::Properties::TTag | ||
| 42 | // [[/codeblock]] | ||
| 43 | // [[/content]] | ||
| 44 | // | ||
| 45 | // ## 2. The local (element-wise) residual | ||
| 46 | // | ||
| 47 | // The local residual assembles the contribution to the residual for | ||
| 48 | // all degrees of freedom associated with an element. Here, we use the | ||
| 49 | // Box method which is based on $P_1$ basis functions (piece-wise linears) | ||
| 50 | // and the degrees of freedom are on the nodes. Each node is associated with | ||
| 51 | // exactly one sub control volume (`scv`) per element and several ($2$ in $\mathbb{R}^2$) | ||
| 52 | // sub control volume faces (`scvf`). In the local residual, we can implement the | ||
| 53 | // contribution for one `scv` (storage and source terms) or one `scvf` (flux terms). | ||
| 54 | // | ||
| 55 | // Let's have a look at the class implementation. | ||
| 56 | // | ||
| 57 | // [[content]] | ||
| 58 | // | ||
| 59 | // The class `DiffusionModelLocalResidual` inherits from something called `DiscretizationDefaultLocalOperator`. | ||
| 60 | // This base class differs depending on the chosen discretization scheme. For the box method | ||
| 61 | // (which is a control-volume finite element scheme) used in this example, | ||
| 62 | // `DiscretizationDefaultLocalOperator` is specialized to `CVFELocalResidual` | ||
| 63 | // in [dumux/discretization/box.hh](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/dumux/discretization/box.hh). | ||
| 64 | // Since the following implementation only works with control-volume finite element schemes due to | ||
| 65 | // the chosen flux implementation, we could have also chosen to | ||
| 66 | // directly inherit from `public CVFELocalResidual<TypeTag>`. | ||
| 67 | namespace Dumux { | ||
| 68 | template<class TypeTag> | ||
| 69 | class DiffusionModelLocalResidual | ||
| 70 | : public DiscretizationDefaultLocalOperator<TypeTag> | ||
| 71 | { | ||
| 72 | // [[exclude]] | ||
| 73 | // the base local operator is selected depending on the chosen discretization scheme | ||
| 74 | using ParentType = DiscretizationDefaultLocalOperator<TypeTag>; | ||
| 75 | |||
| 76 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 77 | using Problem = GetPropType<TypeTag, Properties::Problem>; | ||
| 78 | using NumEqVector = Dumux::NumEqVector<GetPropType<TypeTag, Properties::PrimaryVariables>>; | ||
| 79 | |||
| 80 | using GridVariables = GetPropType<TypeTag, Properties::GridVariables>; | ||
| 81 | using VolumeVariables = typename GridVariables::GridVolumeVariables::VolumeVariables; | ||
| 82 | using ElementVolumeVariables = typename GridVariables::GridVolumeVariables::LocalView; | ||
| 83 | using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView; | ||
| 84 | |||
| 85 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 86 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 87 | using SubControlVolume = typename GridGeometry::SubControlVolume; | ||
| 88 | using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; | ||
| 89 | using GridView = typename GridGeometry::GridView; | ||
| 90 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 91 | |||
| 92 | using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>; | ||
| 93 | using Indices = typename ModelTraits::Indices; | ||
| 94 | static constexpr int dimWorld = GridView::dimensionworld; | ||
| 95 | |||
| 96 | public: | ||
| 97 | 3672 | using ParentType::ParentType; | |
| 98 | // [[/exclude]] | ||
| 99 | // | ||
| 100 | // **Storage term:** Evaluate the rate of change of all conserved quantities | ||
| 101 | // [[codeblock]] | ||
| 102 | 15840 | NumEqVector computeStorage(const Problem& problem, | |
| 103 | const SubControlVolume& scv, | ||
| 104 | const VolumeVariables& volVars) const | ||
| 105 | { | ||
| 106 | 15840 | NumEqVector storage; | |
| 107 | 15840 | storage[Indices::massBalanceEqIdx] = volVars.priVar(Indices::concentrationIdx); | |
| 108 | return storage; | ||
| 109 | } | ||
| 110 | // [[/codeblock]] | ||
| 111 | |||
| 112 | // **Flux term:** Evaluate the fluxes over a face of a sub control volume. | ||
| 113 | // Here we evaluate the (integrated) flux | ||
| 114 | // | ||
| 115 | // ```math | ||
| 116 | // F_{K,\sigma} = -D \sum_{B \in \mathcal{B}_K} c_{h,B} \nabla N_B \cdot\boldsymbol{n} \vert \sigma \vert | ||
| 117 | // ```` | ||
| 118 | // | ||
| 119 | // [[codeblock]] | ||
| 120 | 15840 | NumEqVector computeFlux(const Problem& problem, | |
| 121 | const Element& element, | ||
| 122 | const FVElementGeometry& fvGeometry, | ||
| 123 | const ElementVolumeVariables& elemVolVars, | ||
| 124 | const SubControlVolumeFace& scvf, | ||
| 125 | const ElementFluxVariablesCache& elemFluxVarsCache) const | ||
| 126 | { | ||
| 127 | static_assert(DiscretizationMethods::isCVFE<typename GridGeometry::DiscretizationMethod>, | ||
| 128 | "This local residual is hard-coded to control-volume finite element schemes"); | ||
| 129 | |||
| 130 | // Compute ∇c at the integration point of this sub control volume face. | ||
| 131 | 15840 | const auto& fluxVarCache = elemFluxVarsCache[scvf]; | |
| 132 | 15840 | Dune::FieldVector<Scalar, dimWorld> gradConcentration(0.0); | |
| 133 |
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79200 | for (const auto& scv : scvs(fvGeometry)) |
| 134 | { | ||
| 135 | 63360 | const auto& volVars = elemVolVars[scv]; | |
| 136 | // v.axpy(a, w) means v += a*w | ||
| 137 | 63360 | gradConcentration.axpy( | |
| 138 | 63360 | volVars.priVar(Indices::concentrationIdx), | |
| 139 | 63360 | fluxVarCache.gradN(scv.indexInElement()) | |
| 140 | ); | ||
| 141 | } | ||
| 142 | |||
| 143 | 15840 | NumEqVector flux; | |
| 144 | |||
| 145 | // Compute the flux with `vtmv` (vector transposed times matrix times vector) or -n^T D ∇c A. | ||
| 146 | // The diffusion coefficient comes from the `problem` (see Part 2 of the example). | ||
| 147 | 15840 | flux[Indices::massBalanceEqIdx] = -1.0*vtmv( | |
| 148 | 15840 | scvf.unitOuterNormal(), problem.diffusionCoefficient(), gradConcentration | |
| 149 | 15840 | )*scvf.area(); | |
| 150 | |||
| 151 | 15840 | return flux; | |
| 152 | } | ||
| 153 | }; | ||
| 154 | } // end namespace Dumux | ||
| 155 | // [[/codeblock]] | ||
| 156 | // [[/content]] | ||
| 157 | // | ||
| 158 | // ## 3. The model properties | ||
| 159 | // | ||
| 160 | // By specializing properties for our type tag `DiffusionModel`, | ||
| 161 | // every other class that knows about the type tag (this will be | ||
| 162 | // for example the assembler or the problem), can extract the | ||
| 163 | // type information that we specify here. | ||
| 164 | // | ||
| 165 | // Note that these types can be overwritten for specific problem | ||
| 166 | // definitions if this is needed (we will show this on the next page). | ||
| 167 | // | ||
| 168 | // [[content]] | ||
| 169 | namespace Dumux::Properties { | ||
| 170 | |||
| 171 | // The type of the local residual is the class defined above | ||
| 172 | template<class TypeTag> | ||
| 173 | struct LocalResidual<TypeTag, TTag::DiffusionModel> | ||
| 174 | { using type = DiffusionModelLocalResidual<TypeTag>; }; | ||
| 175 | |||
| 176 | // The default scalar type is double | ||
| 177 | // we compute with double precision floating point numbers | ||
| 178 | template<class TypeTag> | ||
| 179 | struct Scalar<TypeTag, TTag::DiffusionModel> | ||
| 180 | { using type = double; }; | ||
| 181 | |||
| 182 | // The model traits specify some information about our equation system. | ||
| 183 | // Here we have just one equation. We still specify indices so in the | ||
| 184 | // places where we access primary variables, we can do so with a named variable. | ||
| 185 | template<class TypeTag> | ||
| 186 | struct ModelTraits<TypeTag, TTag::DiffusionModel> | ||
| 187 | { | ||
| 188 | struct type | ||
| 189 | { | ||
| 190 | struct Indices | ||
| 191 | { | ||
| 192 | static constexpr int concentrationIdx = 0; | ||
| 193 | static constexpr int massBalanceEqIdx = 0; | ||
| 194 | }; | ||
| 195 | |||
| 196 | static constexpr int numEq() { return 1; } | ||
| 197 | }; | ||
| 198 | }; | ||
| 199 | |||
| 200 | // The primary variable vector has entries of type `Scalar` and is | ||
| 201 | // as large as the number of equations (here 1) but we keep it general. | ||
| 202 | template<class TypeTag> | ||
| 203 | struct PrimaryVariables<TypeTag, TTag::DiffusionModel> | ||
| 204 | { | ||
| 205 | using type = Dune::FieldVector< | ||
| 206 | GetPropType<TypeTag, Properties::Scalar>, | ||
| 207 | GetPropType<TypeTag, Properties::ModelTraits>::numEq() | ||
| 208 | >; | ||
| 209 | }; | ||
| 210 | |||
| 211 | // The `BasicVolumeVariables` are the simplest class of volume variables. | ||
| 212 | // They only store one instance of `PrimaryVariables` for the | ||
| 213 | // degree of freedom (here: vertex dof) that they are attached to. | ||
| 214 | template<class TypeTag> | ||
| 215 | struct VolumeVariables<TypeTag, TTag::DiffusionModel> | ||
| 216 | { | ||
| 217 | struct Traits | ||
| 218 | { | ||
| 219 | using PrimaryVariables | ||
| 220 | = GetPropType<TypeTag, Properties::PrimaryVariables>; | ||
| 221 | }; | ||
| 222 | using type = BasicVolumeVariables<Traits>; | ||
| 223 | }; | ||
| 224 | |||
| 225 | } // end namespace Dumux::Properties | ||
| 226 | // [[/content]] | ||
| 227 | // [[exclude]] | ||
| 228 | #endif | ||
| 229 | // [[/exclude]] | ||
| 230 |