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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 BoxFlux | ||
| 10 | * \brief This file contains the data which is required to calculate | ||
| 11 | * diffusive fluxes due to molecular diffusion with Fick's law. | ||
| 12 | */ | ||
| 13 | #ifndef DUMUX_DISCRETIZATION_BOX_FICKS_LAW_HH | ||
| 14 | #define DUMUX_DISCRETIZATION_BOX_FICKS_LAW_HH | ||
| 15 | |||
| 16 | #include <dune/common/fvector.hh> | ||
| 17 | #include <dune/common/fmatrix.hh> | ||
| 18 | |||
| 19 | #include <dumux/common/math.hh> | ||
| 20 | #include <dumux/common/properties.hh> | ||
| 21 | #include <dumux/discretization/method.hh> | ||
| 22 | #include <dumux/discretization/extrusion.hh> | ||
| 23 | |||
| 24 | #include <dumux/flux/fickiandiffusioncoefficients.hh> | ||
| 25 | #include <dumux/flux/referencesystemformulation.hh> | ||
| 26 | #include <dumux/flux/facetensoraverage.hh> | ||
| 27 | |||
| 28 | namespace Dumux { | ||
| 29 | |||
| 30 | // forward declaration | ||
| 31 | template<class TypeTag, class DiscretizationMethod, ReferenceSystemFormulation referenceSystem> | ||
| 32 | class FicksLawImplementation; | ||
| 33 | |||
| 34 | /*! | ||
| 35 | * \ingroup BoxFlux | ||
| 36 | * \brief Specialization of Fick's Law for the box method. | ||
| 37 | */ | ||
| 38 | template <class TypeTag, ReferenceSystemFormulation referenceSystem> | ||
| 39 | class FicksLawImplementation<TypeTag, DiscretizationMethods::Box, referenceSystem> | ||
| 40 | { | ||
| 41 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 42 | using Problem = GetPropType<TypeTag, Properties::Problem>; | ||
| 43 | using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>; | ||
| 44 | using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>; | ||
| 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 | using Extrusion = Extrusion_t<GridGeometry>; | ||
| 50 | using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView; | ||
| 51 | using GridFluxVariablesCache = GetPropType<TypeTag, Properties::GridFluxVariablesCache>; | ||
| 52 | using ElementFluxVariablesCache = typename GridFluxVariablesCache::LocalView; | ||
| 53 | using FluxVarCache = typename GridFluxVariablesCache::FluxVariablesCache; | ||
| 54 | using BalanceEqOpts = GetPropType<TypeTag, Properties::BalanceEqOpts>; | ||
| 55 | using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView; | ||
| 56 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 57 | using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>; | ||
| 58 | |||
| 59 | enum { dim = GridView::dimension} ; | ||
| 60 | enum { dimWorld = GridView::dimensionworld} ; | ||
| 61 | enum | ||
| 62 | { | ||
| 63 | numPhases = ModelTraits::numFluidPhases(), | ||
| 64 | numComponents = ModelTraits::numFluidComponents() | ||
| 65 | }; | ||
| 66 | using DimWorldMatrix = Dune::FieldMatrix<Scalar, dimWorld, dimWorld>; | ||
| 67 | using ComponentFluxVector = Dune::FieldVector<Scalar, numComponents>; | ||
| 68 | |||
| 69 | public: | ||
| 70 | using DiffusionCoefficientsContainer = FickianDiffusionCoefficients<Scalar, numPhases, numComponents>; | ||
| 71 | |||
| 72 | //return the reference system | ||
| 73 | static constexpr ReferenceSystemFormulation referenceSystemFormulation() | ||
| 74 | { return referenceSystem; } | ||
| 75 | |||
| 76 | /*! | ||
| 77 | * \brief Returns the diffusive fluxes of all components within | ||
| 78 | * a fluid phase across the given sub-control volume face. | ||
| 79 | * The computed fluxes are given in mole/s or kg/s, depending | ||
| 80 | * on the template parameter ReferenceSystemFormulation. | ||
| 81 | */ | ||
| 82 | 405837172 | static ComponentFluxVector flux(const Problem& problem, | |
| 83 | const Element& element, | ||
| 84 | const FVElementGeometry& fvGeometry, | ||
| 85 | const ElementVolumeVariables& elemVolVars, | ||
| 86 | const SubControlVolumeFace& scvf, | ||
| 87 | const int phaseIdx, | ||
| 88 | const ElementFluxVariablesCache& elemFluxVarsCache) | ||
| 89 | { | ||
| 90 | // get inside and outside diffusion tensors and calculate the harmonic mean | ||
| 91 |
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811674344 | const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()]; |
| 92 |
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405837172 | const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()]; |
| 93 | |||
| 94 | // evaluate gradX at integration point and interpolate density | ||
| 95 | 405837172 | const auto& fluxVarsCache = elemFluxVarsCache[scvf]; | |
| 96 | 405837172 | const auto& shapeValues = fluxVarsCache.shapeValues(); | |
| 97 | |||
| 98 | // density interpolation | ||
| 99 | 405837172 | Scalar rho(0.0); | |
| 100 |
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4008146328 | for (auto&& scv : scvs(fvGeometry)) |
| 101 |
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6392943968 | rho += massOrMolarDensity(elemVolVars[scv], referenceSystem, phaseIdx)*shapeValues[scv.indexInElement()][0]; |
| 102 | |||
| 103 | 405837172 | ComponentFluxVector componentFlux(0.0); | |
| 104 |
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1285305540 | for (int compIdx = 0; compIdx < numComponents; compIdx++) |
| 105 | { | ||
| 106 | if constexpr (!FluidSystem::isTracerFluidSystem()) | ||
| 107 |
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928291168 | if (compIdx == FluidSystem::getMainComponent(phaseIdx)) |
| 108 | 401208572 | continue; | |
| 109 | |||
| 110 | 486339796 | const auto diffCoeff = averageDiffusionCoefficient_(phaseIdx, compIdx, insideVolVars, outsideVolVars, problem, scvf); | |
| 111 | |||
| 112 | // compute the diffusive flux | ||
| 113 |
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3459017944 | const auto massOrMoleFrac = [&](const SubControlVolume& scv){ return massOrMoleFraction(elemVolVars[scv], referenceSystem, phaseIdx, compIdx); }; |
| 114 |
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486339796 | componentFlux[compIdx] = discreteFlux_(fvGeometry, scvf, fluxVarsCache, massOrMoleFrac, diffCoeff, rho); |
| 115 | |||
| 116 | // if the main component is balanced subtract the same flux from there (conservation) | ||
| 117 | if constexpr (!FluidSystem::isTracerFluidSystem()) | ||
| 118 |
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470179796 | if (BalanceEqOpts::mainComponentIsBalanced(phaseIdx)) |
| 119 |
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1433396788 | componentFlux[FluidSystem::getMainComponent(phaseIdx)] -= componentFlux[compIdx]; |
| 120 | } | ||
| 121 | 405837172 | return componentFlux; | |
| 122 | } | ||
| 123 | |||
| 124 | // compute transmissibilities ti for analytical jacobians | ||
| 125 | static std::array<std::vector<Scalar>, numComponents> | ||
| 126 | 20000 | calculateTransmissibilities(const Problem& problem, | |
| 127 | const Element& element, | ||
| 128 | const FVElementGeometry& fvGeometry, | ||
| 129 | const ElementVolumeVariables& elemVolVars, | ||
| 130 | const SubControlVolumeFace& scvf, | ||
| 131 | const FluxVarCache& fluxVarCache, | ||
| 132 | const int phaseIdx) | ||
| 133 | { | ||
| 134 | 20000 | Scalar rho(0.0); | |
| 135 | 20000 | const auto& shapeValues = fluxVarCache.shapeValues(); | |
| 136 |
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200000 | for (auto&& scv : scvs(fvGeometry)) |
| 137 | 320000 | rho += massOrMolarDensity(elemVolVars[scv], referenceSystem, phaseIdx)*shapeValues[scv.indexInElement()][0]; | |
| 138 | |||
| 139 |
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40000 | const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()]; |
| 140 |
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20000 | const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()]; |
| 141 | |||
| 142 | 20000 | std::array<std::vector<Scalar>, numComponents> ti; | |
| 143 |
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60000 | for (int compIdx = 0; compIdx < numComponents; compIdx++) |
| 144 | { | ||
| 145 | if constexpr (!FluidSystem::isTracerFluidSystem()) | ||
| 146 | if (compIdx == FluidSystem::getMainComponent(phaseIdx)) | ||
| 147 | continue; | ||
| 148 | |||
| 149 | 80000 | const auto diffCoeff = averageDiffusionCoefficient_(phaseIdx, compIdx, insideVolVars, outsideVolVars, problem, scvf); | |
| 150 | |||
| 151 |
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80000 | ti[compIdx].resize(fvGeometry.numScv()); |
| 152 |
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400000 | for (auto&& scv : scvs(fvGeometry)) |
| 153 | 1120000 | ti[compIdx][scv.indexInElement()] = -rho*vtmv(scvf.unitOuterNormal(), diffCoeff, fluxVarCache.gradN(scv.indexInElement()))*Extrusion::area(fvGeometry, scvf); | |
| 154 | } | ||
| 155 | |||
| 156 | 20000 | return ti; | |
| 157 | } | ||
| 158 | |||
| 159 | private: | ||
| 160 | ✗ | static Scalar averageDiffusionCoefficient_(const int phaseIdx, const int compIdx, | |
| 161 | const VolumeVariables& insideVV, const VolumeVariables& outsideVV, | ||
| 162 | const Problem& problem, | ||
| 163 | const SubControlVolumeFace& scvf) | ||
| 164 | { | ||
| 165 | // effective diffusion tensors | ||
| 166 |
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8120000 | auto [insideDiffCoeff, outsideDiffCoeff] = diffusionCoefficientsAtInterface_(phaseIdx, compIdx, insideVV, outsideVV); |
| 167 | |||
| 168 | // scale by extrusion factor | ||
| 169 | 8120000 | insideDiffCoeff *= insideVV.extrusionFactor(); | |
| 170 | 8120000 | outsideDiffCoeff *= outsideVV.extrusionFactor(); | |
| 171 | |||
| 172 | // the resulting averaged diffusion tensor | ||
| 173 |
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20300000 | return faceTensorAverage(insideDiffCoeff, outsideDiffCoeff, scvf.unitOuterNormal()); |
| 174 | } | ||
| 175 | |||
| 176 | static std::pair<Scalar, Scalar> | ||
| 177 | 470179796 | diffusionCoefficientsAtInterface_([[maybe_unused]] const int phaseIdx, const int compIdx, | |
| 178 | const VolumeVariables& insideVV, const VolumeVariables& outsideVV) | ||
| 179 | { | ||
| 180 | if constexpr (!FluidSystem::isTracerFluidSystem()) | ||
| 181 | { | ||
| 182 |
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470179796 | const auto mainCompIdx = FluidSystem::getMainComponent(phaseIdx); |
| 183 | 470179796 | const auto insideDiffCoeff = insideVV.effectiveDiffusionCoefficient(phaseIdx, mainCompIdx, compIdx); | |
| 184 | 470179796 | const auto outsideDiffCoeff = outsideVV.effectiveDiffusionCoefficient(phaseIdx, mainCompIdx, compIdx); | |
| 185 | 940359592 | return { std::move(insideDiffCoeff), std::move(outsideDiffCoeff) }; | |
| 186 | } | ||
| 187 | else | ||
| 188 | { | ||
| 189 |
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8120000 | const auto insideDiffCoeff = insideVV.effectiveDiffusionCoefficient(0, 0, compIdx); |
| 190 |
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8120000 | const auto outsideDiffCoeff = outsideVV.effectiveDiffusionCoefficient(0, 0, compIdx); |
| 191 |
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16240000 | return { std::move(insideDiffCoeff), std::move(outsideDiffCoeff) }; |
| 192 | } | ||
| 193 | } | ||
| 194 | |||
| 195 | template<class EvaluateVariable, class Tensor> | ||
| 196 | 471039534 | static Scalar discreteFlux_(const FVElementGeometry& fvGeometry, | |
| 197 | const SubControlVolumeFace& scvf, | ||
| 198 | const FluxVarCache& fluxVarsCache, | ||
| 199 | const EvaluateVariable& massOrMoleFraction, | ||
| 200 | const Tensor& D, const Scalar preFactor) | ||
| 201 | { | ||
| 202 | 471039534 | Dune::FieldVector<Scalar, dimWorld> gradX(0.0); | |
| 203 |
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4512736564 | for (auto&& scv : scvs(fvGeometry)) |
| 204 | 5415713104 | gradX.axpy(massOrMoleFraction(scv), fluxVarsCache.gradN(scv.indexInElement())); | |
| 205 | 1040870684 | return -1.0*preFactor*vtmv(scvf.unitOuterNormal(), D, gradX)*Extrusion::area(fvGeometry, scvf); | |
| 206 | } | ||
| 207 | }; | ||
| 208 | |||
| 209 | } // end namespace Dumux | ||
| 210 | |||
| 211 | #endif | ||
| 212 |