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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 DispersionTensors | ||
| 10 | * \brief Scheidegger's dispersion tensor | ||
| 11 | */ | ||
| 12 | |||
| 13 | #ifndef DUMUX_MATERIAL_FLUIDMATRIX_DISPERSIONTENSORS_SCHEIDEGGER_HH | ||
| 14 | #define DUMUX_MATERIAL_FLUIDMATRIX_DISPERSIONTENSORS_SCHEIDEGGER_HH | ||
| 15 | |||
| 16 | #include <algorithm> | ||
| 17 | #include <cmath> | ||
| 18 | #include <dune/common/math.hh> | ||
| 19 | #include <dune/common/std/type_traits.hh> | ||
| 20 | #include <dune/common/fmatrix.hh> | ||
| 21 | #include <dumux/common/properties.hh> | ||
| 22 | #include <dumux/common/parameters.hh> | ||
| 23 | #include <dumux/discretization/method.hh> | ||
| 24 | #include <dumux/flux/facetensoraverage.hh> | ||
| 25 | #include <dumux/flux/traits.hh> | ||
| 26 | |||
| 27 | namespace Dumux { | ||
| 28 | |||
| 29 | namespace Detail { | ||
| 30 | template <class Problem, class SubControlVolumeFace> | ||
| 31 | using HasVelocityInSpatialParams = decltype(std::declval<Problem>().spatialParams().velocity(std::declval<SubControlVolumeFace>())); | ||
| 32 | |||
| 33 | template<class Problem, class SubControlVolumeFace> | ||
| 34 | static constexpr bool hasVelocityInSpatialParams() | ||
| 35 | { return Dune::Std::is_detected<HasVelocityInSpatialParams, Problem, SubControlVolumeFace>::value; } | ||
| 36 | } | ||
| 37 | |||
| 38 | /*! | ||
| 39 | * \addtogroup DispersionTensors | ||
| 40 | * \copydetails Dumux::ScheideggersDispersionTensor | ||
| 41 | */ | ||
| 42 | |||
| 43 | /*! | ||
| 44 | * \ingroup DispersionTensors | ||
| 45 | * \brief Scheidegger's dispersion tensor | ||
| 46 | * | ||
| 47 | * ### Scheidegger's dispersion tensor | ||
| 48 | * This class calculates the dispersion tensor for compositional and thermal models using Scheidegger's model. | ||
| 49 | * The dispersion tensor is given by: | ||
| 50 | * \f[ | ||
| 51 | * D = \frac{\mathbf{v} \mathbf{v}^T}{\|\mathbf{v}\|} \cdot (\alpha_L - \alpha_T) + \|\mathbf{v}\| \cdot \alpha_T \cdot \mathbf{I} | ||
| 52 | * \f] | ||
| 53 | * where \f$\mathbf{v}\f$ is the velocity vector, \f$\alpha_L\f$ and \f$\alpha_T\f$ are the | ||
| 54 | * longitudinal and transverse dispersivities, respectively, and \f$\mathbf{I}\f$ is the identity matrix. | ||
| 55 | * The velocity is either taken from the spatial parameters or from the reconstructed velocity field and the dispersivities are taken from the spatial parameters. | ||
| 56 | */ | ||
| 57 | template<class TypeTag> | ||
| 58 | class ScheideggersDispersionTensor | ||
| 59 | { | ||
| 60 | using Problem = GetPropType<TypeTag, Properties::Problem>; | ||
| 61 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 62 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 63 | using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; | ||
| 64 | using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView; | ||
| 65 | |||
| 66 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 67 | using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView; | ||
| 68 | static const int dimWorld = GridView::dimensionworld; | ||
| 69 | using DimWorldMatrix = Dune::FieldMatrix<Scalar, dimWorld, dimWorld>; | ||
| 70 | |||
| 71 | using FluxVariables = GetPropType<TypeTag, Properties::FluxVariables>; | ||
| 72 | using FluxTraits = typename Dumux::FluxTraits<FluxVariables>; | ||
| 73 | static constexpr bool stationaryVelocityField = FluxTraits::hasStationaryVelocityField(); | ||
| 74 | |||
| 75 | public: | ||
| 76 | template <class ElementFluxVariablesCache> | ||
| 77 | 7044400 | static DimWorldMatrix compositionalDispersionTensor(const Problem& problem, | |
| 78 | const SubControlVolumeFace& scvf, | ||
| 79 | const FVElementGeometry& fvGeometry, | ||
| 80 | const ElementVolumeVariables& elemVolVars, | ||
| 81 | const ElementFluxVariablesCache& elemFluxVarsCache, | ||
| 82 | const int phaseIdx, | ||
| 83 | const int compIdx) | ||
| 84 | { | ||
| 85 |
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7044400 | if (phaseIdx > 0) |
| 86 | ✗ | DUNE_THROW(Dune::NotImplemented, "Scheidegger dispersion tensors are only implemented for single phase flows."); | |
| 87 | |||
| 88 | // Get the velocity either from the reconstruction, or from the spatialparams | ||
| 89 | 7044400 | auto velocity = dispersionVelocity_(problem, scvf, fvGeometry, elemVolVars, elemFluxVarsCache); | |
| 90 | |||
| 91 | // collect the dispersion alphas at this location | ||
| 92 | 7044400 | std::array<Scalar,2> dispersivity = problem.spatialParams().dispersionAlphas(scvf.center(), phaseIdx, compIdx); | |
| 93 | |||
| 94 | 7044400 | return scheideggerDispersionTensor_(dispersivity, velocity); | |
| 95 | } | ||
| 96 | |||
| 97 | template <class ElementFluxVariablesCache> | ||
| 98 | 2083200 | static DimWorldMatrix thermalDispersionTensor(const Problem& problem, | |
| 99 | const SubControlVolumeFace& scvf, | ||
| 100 | const FVElementGeometry& fvGeometry, | ||
| 101 | const ElementVolumeVariables& elemVolVars, | ||
| 102 | const ElementFluxVariablesCache& elemFluxVarsCache, | ||
| 103 | const int phaseIdx) | ||
| 104 | { | ||
| 105 |
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2083200 | if (phaseIdx > 0) |
| 106 | ✗ | DUNE_THROW(Dune::NotImplemented, "Scheidegger dispersion tensors are only implemented for single phase flows."); | |
| 107 | |||
| 108 | // Get the velocity either from the reconstruction, or from the spatialparams | ||
| 109 | 2083200 | auto velocity = dispersionVelocity_(problem, scvf, fvGeometry, elemVolVars, elemFluxVarsCache); | |
| 110 | |||
| 111 | // collect the dispersion alphas at this location | ||
| 112 | 2083200 | std::array<Scalar,2> dispersivity = problem.spatialParams().dispersionAlphas(scvf.center(), phaseIdx); //TODO: fix this? | |
| 113 | |||
| 114 | 2083200 | return scheideggerDispersionTensor_(dispersivity, velocity); | |
| 115 | } | ||
| 116 | |||
| 117 | private: | ||
| 118 | |||
| 119 | template <class ElementFluxVariablesCache> | ||
| 120 | 9127600 | static Dune::FieldVector<Scalar, dimWorld> dispersionVelocity_(const Problem& problem, | |
| 121 | const SubControlVolumeFace& scvf, | ||
| 122 | [[maybe_unused]] const FVElementGeometry& fvGeometry, | ||
| 123 | [[maybe_unused]] const ElementVolumeVariables& elemVolVars, | ||
| 124 | [[maybe_unused]] const ElementFluxVariablesCache& elemFluxVarsCache) | ||
| 125 | { | ||
| 126 | // Calculate Darcy's velocity | ||
| 127 |
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5128000 | Dune::FieldVector<Scalar, dimWorld> velocity(0.0); |
| 128 | if constexpr (stationaryVelocityField) | ||
| 129 | { | ||
| 130 | if constexpr (!Detail::hasVelocityInSpatialParams<Problem,SubControlVolumeFace>() ) | ||
| 131 | DUNE_THROW(Dune::NotImplemented, "\n Please provide the stationary velocity field in the spatialparams via a velocity function."); | ||
| 132 | else | ||
| 133 | 3999600 | velocity = problem.spatialParams().velocity(scvf); | |
| 134 | } | ||
| 135 | else | ||
| 136 | { | ||
| 137 | if constexpr (FVElementGeometry::GridGeometry::discMethod == DiscretizationMethods::box) | ||
| 138 | { | ||
| 139 |
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5128000 | const auto& fluxVarsCache = elemFluxVarsCache[scvf]; |
| 140 |
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5128000 | const auto& shapeValues = fluxVarsCache.shapeValues(); |
| 141 | |||
| 142 | // get inside and outside permeability tensors and calculate the harmonic mean | ||
| 143 |
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5128000 | const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()]; |
| 144 |
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5128000 | const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()]; |
| 145 | 10256000 | const auto K = faceTensorAverage(insideVolVars.permeability(), | |
| 146 | 5128000 | outsideVolVars.permeability(), | |
| 147 |
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5128000 | scvf.unitOuterNormal()); |
| 148 | |||
| 149 | // evaluate gradP - rho*g at integration point | ||
| 150 | 5128000 | Dune::FieldVector<Scalar, dimWorld> gradP(0.0); | |
| 151 | 5128000 | Scalar rho(0.0); | |
| 152 |
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5128000 | static const bool enableGravity = getParamFromGroup<bool>(problem.paramGroup(), "Problem.EnableGravity"); |
| 153 |
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25640000 | for (auto&& scv : scvs(fvGeometry)) |
| 154 | { | ||
| 155 | 20512000 | const auto& volVars = elemVolVars[scv]; | |
| 156 | |||
| 157 |
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20512000 | if (enableGravity) |
| 158 | 20512000 | rho += volVars.density(0)*shapeValues[scv.indexInElement()][0]; | |
| 159 | // the global shape function gradient | ||
| 160 | 41024000 | gradP.axpy(volVars.pressure(0), fluxVarsCache.gradN(scv.indexInElement())); | |
| 161 | } | ||
| 162 | |||
| 163 |
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5128000 | if (enableGravity) |
| 164 | 5128000 | gradP.axpy(-rho, problem.spatialParams().gravity(scvf.center())); | |
| 165 | |||
| 166 | 5128000 | velocity = gradP; | |
| 167 | 5128000 | velocity *= K; | |
| 168 | |||
| 169 | 5128000 | velocity /= -0.5 * (insideVolVars.viscosity() + outsideVolVars.viscosity()); | |
| 170 | } | ||
| 171 | else | ||
| 172 | DUNE_THROW(Dune::NotImplemented, "\n Scheidegger Dispersion for compositional models without given constant velocity field is only implemented using the Box method."); | ||
| 173 | } | ||
| 174 | |||
| 175 | 9127600 | return velocity; | |
| 176 | } | ||
| 177 | |||
| 178 | 9127600 | static DimWorldMatrix scheideggerDispersionTensor_(const std::array<Scalar,2>& dispersivity, | |
| 179 | const Dune::FieldVector<Scalar, dimWorld>& velocity) | ||
| 180 | { | ||
| 181 | 9127600 | DimWorldMatrix dispersionTensor(0.0); | |
| 182 | |||
| 183 | //matrix multiplication of the velocity at the interface: vv^T | ||
| 184 |
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27382800 | for (int i=0; i < dimWorld; i++) |
| 185 |
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54765600 | for (int j = 0; j < dimWorld; j++) |
| 186 | 36510400 | dispersionTensor[i][j] = velocity[i]*velocity[j]; | |
| 187 | |||
| 188 | //normalize velocity product --> vv^T/||v||, [m/s] | ||
| 189 | 9127600 | Scalar vNorm = velocity.two_norm(); | |
| 190 | |||
| 191 | 9127600 | dispersionTensor /= vNorm; | |
| 192 |
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9127600 | if (vNorm < 1e-20) |
| 193 | 9127600 | dispersionTensor = 0; | |
| 194 | |||
| 195 | //multiply with dispersivity difference: vv^T/||v||*(alphaL - alphaT), [m^2/s] --> alphaL = longitudinal disp., alphaT = transverse disp. | ||
| 196 | 9127600 | dispersionTensor *= (dispersivity[0] - dispersivity[1]); | |
| 197 | |||
| 198 | //add ||v||*alphaT to the main diagonal:vv^T/||v||*(alphaL - alphaT) + ||v||*alphaT, [m^2/s] | ||
| 199 |
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27382800 | for (int i = 0; i < dimWorld; i++) |
| 200 | 18255200 | dispersionTensor[i][i] += vNorm*dispersivity[1]; | |
| 201 | |||
| 202 | 9127600 | return dispersionTensor; | |
| 203 | } | ||
| 204 | |||
| 205 | }; | ||
| 206 | |||
| 207 | } // end namespace Dumux | ||
| 208 | |||
| 209 | #endif | ||
| 210 |