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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 CCTpfaFlux | ||
| 10 | * \brief Fick's law for cell-centered finite volume schemes with two-point flux approximation | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_DISCRETIZATION_CC_TPFA_FICKS_LAW_HH | ||
| 13 | #define DUMUX_DISCRETIZATION_CC_TPFA_FICKS_LAW_HH | ||
| 14 | |||
| 15 | #include <dune/common/fvector.hh> | ||
| 16 | |||
| 17 | #include <dumux/common/parameters.hh> | ||
| 18 | #include <dumux/common/properties.hh> | ||
| 19 | |||
| 20 | #include <dumux/discretization/method.hh> | ||
| 21 | #include <dumux/discretization/extrusion.hh> | ||
| 22 | #include <dumux/discretization/cellcentered/tpfa/computetransmissibility.hh> | ||
| 23 | #include <dumux/flux/fickiandiffusioncoefficients.hh> | ||
| 24 | |||
| 25 | #include <dumux/flux/referencesystemformulation.hh> | ||
| 26 | |||
| 27 | namespace Dumux { | ||
| 28 | |||
| 29 | // forward declaration | ||
| 30 | template<class TypeTag, class DiscretizationMethod, ReferenceSystemFormulation referenceSystem> | ||
| 31 | class FicksLawImplementation; | ||
| 32 | |||
| 33 | /*! | ||
| 34 | * \ingroup CCTpfaFlux | ||
| 35 | * \brief Fick's law for cell-centered finite volume schemes with two-point flux approximation | ||
| 36 | */ | ||
| 37 | template <class TypeTag, ReferenceSystemFormulation referenceSystem> | ||
| 38 | class FicksLawImplementation<TypeTag, DiscretizationMethods::CCTpfa, referenceSystem> | ||
| 39 | { | ||
| 40 | using Implementation = FicksLawImplementation<TypeTag, DiscretizationMethods::CCTpfa, referenceSystem>; | ||
| 41 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 42 | using Problem = GetPropType<TypeTag, Properties::Problem>; | ||
| 43 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 44 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 45 | using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; | ||
| 46 | using Extrusion = Extrusion_t<GridGeometry>; | ||
| 47 | using GridView = typename GridGeometry::GridView; | ||
| 48 | using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView; | ||
| 49 | using VolumeVariables = typename ElementVolumeVariables::VolumeVariables; | ||
| 50 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 51 | using GridFluxVariablesCache = GetPropType<TypeTag, Properties::GridFluxVariablesCache>; | ||
| 52 | using ElementFluxVariablesCache = typename GridFluxVariablesCache::LocalView; | ||
| 53 | using FluxVariablesCache = typename GridFluxVariablesCache::FluxVariablesCache; | ||
| 54 | using BalanceEqOpts = GetPropType<TypeTag, Properties::BalanceEqOpts>; | ||
| 55 | |||
| 56 | using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>; | ||
| 57 | static const int dim = GridView::dimension; | ||
| 58 | static const int dimWorld = GridView::dimensionworld; | ||
| 59 | static const int numPhases = ModelTraits::numFluidPhases(); | ||
| 60 | static const int numComponents = ModelTraits::numFluidComponents(); | ||
| 61 | |||
| 62 | using ComponentFluxVector = Dune::FieldVector<Scalar, numComponents>; | ||
| 63 | |||
| 64 | //! Class that fills the cache corresponding to tpfa Fick's Law | ||
| 65 | class TpfaFicksLawCacheFiller | ||
| 66 | { | ||
| 67 | public: | ||
| 68 | //! Function to fill a TpfaFicksLawCache of a given scvf | ||
| 69 | //! This interface has to be met by any diffusion-related cache filler class | ||
| 70 | template<class FluxVariablesCacheFiller> | ||
| 71 | ✗ | static void fill(FluxVariablesCache& scvfFluxVarsCache, | |
| 72 | unsigned int phaseIdx, unsigned int compIdx, | ||
| 73 | const Problem& problem, | ||
| 74 | const Element& element, | ||
| 75 | const FVElementGeometry& fvGeometry, | ||
| 76 | const ElementVolumeVariables& elemVolVars, | ||
| 77 | const SubControlVolumeFace& scvf, | ||
| 78 | const FluxVariablesCacheFiller& fluxVarsCacheFiller) | ||
| 79 | { | ||
| 80 | 477869064 | scvfFluxVarsCache.updateDiffusion(problem, element, fvGeometry, elemVolVars, scvf, phaseIdx, compIdx); | |
| 81 | ✗ | } | |
| 82 | }; | ||
| 83 | |||
| 84 | //! Class that caches the transmissibility | ||
| 85 | class TpfaFicksLawCache | ||
| 86 | { | ||
| 87 | public: | ||
| 88 | using Filler = TpfaFicksLawCacheFiller; | ||
| 89 | |||
| 90 | void updateDiffusion(const Problem& problem, | ||
| 91 | const Element& element, | ||
| 92 | const FVElementGeometry& fvGeometry, | ||
| 93 | const ElementVolumeVariables& elemVolVars, | ||
| 94 | const SubControlVolumeFace &scvf, | ||
| 95 | const unsigned int phaseIdx, | ||
| 96 | const unsigned int compIdx) | ||
| 97 | { | ||
| 98 | 236336076 | tij_[phaseIdx][compIdx] = Implementation::calculateTransmissibility(problem, element, fvGeometry, elemVolVars, scvf, phaseIdx, compIdx); | |
| 99 | } | ||
| 100 | |||
| 101 | const Scalar& diffusionTij(unsigned int phaseIdx, unsigned int compIdx) const | ||
| 102 |
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213786500 | { return tij_[phaseIdx][compIdx]; } |
| 103 | |||
| 104 | private: | ||
| 105 | std::array< std::array<Scalar, numComponents>, numPhases> tij_; | ||
| 106 | }; | ||
| 107 | |||
| 108 | public: | ||
| 109 | using DiscretizationMethod = DiscretizationMethods::CCTpfa; | ||
| 110 | //! state the discretization method this implementation belongs to | ||
| 111 | static constexpr DiscretizationMethod discMethod{}; | ||
| 112 | |||
| 113 | //! Return the reference system | ||
| 114 | static constexpr ReferenceSystemFormulation referenceSystemFormulation() | ||
| 115 | { return referenceSystem; } | ||
| 116 | |||
| 117 | //! state the type for the corresponding cache and its filler | ||
| 118 | using Cache = TpfaFicksLawCache; | ||
| 119 | |||
| 120 | using DiffusionCoefficientsContainer = FickianDiffusionCoefficients<Scalar, numPhases, numComponents>; | ||
| 121 | |||
| 122 | /*! | ||
| 123 | * \brief Returns the diffusive fluxes of all components within | ||
| 124 | * a fluid phase across the given sub-control volume face. | ||
| 125 | * The computed fluxes are given in mole/s or kg/s, depending | ||
| 126 | * on the template parameter ReferenceSystemFormulation. | ||
| 127 | * | ||
| 128 | * \note This overload allows to explicitly specify the inside and outside volume variables | ||
| 129 | * which can be useful to evaluate diffusive fluxes at boundaries with given outside values. | ||
| 130 | * This only works if scvf.numOutsideScv() == 1. | ||
| 131 | */ | ||
| 132 | static ComponentFluxVector flux(const Problem& problem, | ||
| 133 | const Element& element, | ||
| 134 | const FVElementGeometry& fvGeometry, | ||
| 135 | const VolumeVariables& insideVolVars, | ||
| 136 | const VolumeVariables& outsideVolVars, | ||
| 137 | const SubControlVolumeFace& scvf, | ||
| 138 | const int phaseIdx, | ||
| 139 | const ElementFluxVariablesCache& elemFluxVarsCache) | ||
| 140 | { | ||
| 141 | if constexpr (isMixedDimensional_) | ||
| 142 | if (scvf.numOutsideScv() != 1) | ||
| 143 | DUNE_THROW(Dune::Exception, "This flux overload requires scvf.numOutsideScv() == 1"); | ||
| 144 | |||
| 145 | // helper lambda to get the outside mole or mass fraction | ||
| 146 | const auto getOutsideX = [&](const Scalar xInside, const Scalar tij, const int phaseIdx, const int compIdx) | ||
| 147 | { | ||
| 148 | return massOrMoleFraction(outsideVolVars, referenceSystem, phaseIdx, compIdx); | ||
| 149 | }; | ||
| 150 | |||
| 151 | // helper lambda to get the averaged density at the scvf | ||
| 152 | const auto getRho = [&](const int phaseIdx, const Scalar rhoInside, const Scalar rhoOutside) | ||
| 153 | { | ||
| 154 | return 0.5*(rhoInside + rhoOutside); | ||
| 155 | }; | ||
| 156 | |||
| 157 | return flux_(element, fvGeometry, insideVolVars, outsideVolVars, elemFluxVarsCache, scvf, phaseIdx, getOutsideX, getRho); | ||
| 158 | } | ||
| 159 | |||
| 160 | |||
| 161 | /*! | ||
| 162 | * \brief Returns the diffusive fluxes of all components within | ||
| 163 | * a fluid phase across the given sub-control volume face. | ||
| 164 | * The computed fluxes are given in mole/s or kg/s, depending | ||
| 165 | * on the template parameter ReferenceSystemFormulation. | ||
| 166 | */ | ||
| 167 | 14598246 | static ComponentFluxVector flux(const Problem& problem, | |
| 168 | const Element& element, | ||
| 169 | const FVElementGeometry& fvGeometry, | ||
| 170 | const ElementVolumeVariables& elemVolVars, | ||
| 171 | const SubControlVolumeFace& scvf, | ||
| 172 | const int phaseIdx, | ||
| 173 | const ElementFluxVariablesCache& elemFluxVarsCache) | ||
| 174 | { | ||
| 175 | // get inside/outside volume variables | ||
| 176 | 29196492 | const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()]; | |
| 177 | 29196492 | const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()]; | |
| 178 | |||
| 179 | // helper lambda to get the outside mole or mass fraction | ||
| 180 | 17565312 | const auto getOutsideX = [&](const Scalar xInside, const Scalar tij, const int phaseIdx, const int compIdx) | |
| 181 | { | ||
| 182 |
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6926266 | const Scalar massOrMoleFractionOutside = massOrMoleFraction(outsideVolVars, referenceSystem, phaseIdx, compIdx); |
| 183 | if constexpr (isMixedDimensional_) | ||
| 184 | { | ||
| 185 |
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5934132 | return scvf.numOutsideScvs() == 1 ? massOrMoleFractionOutside |
| 186 | 82452 | : branchingFacetX_(problem, element, fvGeometry, elemVolVars, | |
| 187 | 82452 | elemFluxVarsCache, scvf, xInside, tij, phaseIdx, compIdx); | |
| 188 | } | ||
| 189 | else | ||
| 190 | ✗ | return massOrMoleFractionOutside; | |
| 191 | }; | ||
| 192 | |||
| 193 | // helper lambda to get the averaged density at the scvf | ||
| 194 | 5899136 | const auto getRho = [&](const int phaseIdx, const Scalar rhoInside, const Scalar rhoOutside) | |
| 195 | { | ||
| 196 | if constexpr (isMixedDimensional_) | ||
| 197 | { | ||
| 198 |
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2967066 | return scvf.numOutsideScvs() == 1 ? 0.5*(rhoInside + rhoOutside) |
| 199 | 82452 | : branchingFacetDensity_(elemVolVars, scvf, phaseIdx, rhoInside); | |
| 200 | } | ||
| 201 | else | ||
| 202 | 214177346 | return 0.5*(rhoInside + rhoOutside); | |
| 203 | }; | ||
| 204 | |||
| 205 |
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14598246 | return flux_(element, fvGeometry, insideVolVars, outsideVolVars, elemFluxVarsCache, scvf, phaseIdx, getOutsideX, getRho); |
| 206 | } | ||
| 207 | |||
| 208 | //! compute diffusive transmissibilities | ||
| 209 | 246694810 | static Scalar calculateTransmissibility(const Problem& problem, | |
| 210 | const Element& element, | ||
| 211 | const FVElementGeometry& fvGeometry, | ||
| 212 | const ElementVolumeVariables& elemVolVars, | ||
| 213 | const SubControlVolumeFace& scvf, | ||
| 214 | const int phaseIdx, const int compIdx) | ||
| 215 | { | ||
| 216 | |||
| 217 | |||
| 218 |
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246694810 | const auto insideScvIdx = scvf.insideScvIdx(); |
| 219 |
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246694810 | const auto& insideScv = fvGeometry.scv(insideScvIdx); |
| 220 | 246694810 | const auto& insideVolVars = elemVolVars[insideScvIdx]; | |
| 221 | 340573642 | const auto getDiffCoeff = [&](const auto& vv) | |
| 222 | { | ||
| 223 | using FluidSystem = typename ElementVolumeVariables::VolumeVariables::FluidSystem; | ||
| 224 | if constexpr (FluidSystem::isTracerFluidSystem()) | ||
| 225 | 116583472 | return vv.effectiveDiffusionCoefficient(0, 0, compIdx); | |
| 226 | else | ||
| 227 |
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72425552 | return vv.effectiveDiffusionCoefficient(phaseIdx, FluidSystem::getMainComponent(phaseIdx), compIdx); |
| 228 | }; | ||
| 229 | |||
| 230 | 246694810 | const auto insideDiffCoeff = getDiffCoeff(insideVolVars); | |
| 231 | |||
| 232 | 246694810 | const Scalar ti = computeTpfaTransmissibility(fvGeometry, scvf, insideScv, insideDiffCoeff, insideVolVars.extrusionFactor()); | |
| 233 | |||
| 234 | // for the boundary (dirichlet) or at branching points we only need ti | ||
| 235 | Scalar tij; | ||
| 236 |
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246694810 | if (scvf.boundary() || scvf.numOutsideScvs() > 1) |
| 237 | 14757900 | tij = Extrusion::area(fvGeometry, scvf)*ti; | |
| 238 | |||
| 239 | // otherwise we compute a tpfa harmonic mean | ||
| 240 | else | ||
| 241 | { | ||
| 242 |
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239315860 | const auto outsideScvIdx = scvf.outsideScvIdx(); |
| 243 |
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239315860 | const auto& outsideScv = fvGeometry.scv(outsideScvIdx); |
| 244 | 239315860 | const auto& outsideVolVars = elemVolVars[outsideScvIdx]; | |
| 245 | 239315860 | const auto outsideDiffCoeff = getDiffCoeff(outsideVolVars); | |
| 246 | |||
| 247 | Scalar tj; | ||
| 248 | if constexpr (dim == dimWorld) | ||
| 249 | // assume the normal vector from outside is anti parallel so we save flipping a vector | ||
| 250 | 234166616 | tj = -1.0*computeTpfaTransmissibility(fvGeometry, scvf, outsideScv, outsideDiffCoeff, outsideVolVars.extrusionFactor()); | |
| 251 | else | ||
| 252 | 5161888 | tj = computeTpfaTransmissibility(fvGeometry, fvGeometry.flipScvf(scvf.index()), | |
| 253 | outsideScv, | ||
| 254 | outsideDiffCoeff, | ||
| 255 | outsideVolVars.extrusionFactor()); | ||
| 256 | |||
| 257 | // check if we are dividing by zero! | ||
| 258 |
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239315860 | if (ti*tj <= 0.0) |
| 259 | tij = 0; | ||
| 260 | else | ||
| 261 | 275446116 | tij = Extrusion::area(fvGeometry, scvf)*(ti * tj)/(ti + tj); | |
| 262 | } | ||
| 263 | |||
| 264 | 246694810 | return tij; | |
| 265 | } | ||
| 266 | |||
| 267 | private: | ||
| 268 | template<class OutsideFractionHelper, class DensityHelper> | ||
| 269 | 220944836 | static ComponentFluxVector flux_(const Element& element, | |
| 270 | const FVElementGeometry& fvGeometry, | ||
| 271 | const VolumeVariables& insideVolVars, | ||
| 272 | const VolumeVariables& outsideVolVars, | ||
| 273 | const ElementFluxVariablesCache& elemFluxVarsCache, | ||
| 274 | const SubControlVolumeFace& scvf, | ||
| 275 | const int phaseIdx, | ||
| 276 | const OutsideFractionHelper& getOutsideX, | ||
| 277 | const DensityHelper& getRho) | ||
| 278 | { | ||
| 279 | 220944836 | ComponentFluxVector componentFlux(0.0); | |
| 280 |
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661085604 | for (int compIdx = 0; compIdx < numComponents; compIdx++) |
| 281 | { | ||
| 282 | using FluidSystem = typename VolumeVariables::FluidSystem; | ||
| 283 | if constexpr (!FluidSystem::isTracerFluidSystem()) | ||
| 284 |
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439291240 | if (compIdx == FluidSystem::getMainComponent(phaseIdx)) |
| 285 | continue; | ||
| 286 | |||
| 287 | // diffusion tensors are always solution dependent | ||
| 288 |
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288366860 | const Scalar tij = elemFluxVarsCache[scvf].diffusionTij(phaseIdx, compIdx); |
| 289 | |||
| 290 | // the inside and outside mass/mole fractions fractions | ||
| 291 |
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230633746 | const Scalar xInside = massOrMoleFraction(insideVolVars, referenceSystem, phaseIdx, compIdx); |
| 292 |
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230633746 | const Scalar xOutside = getOutsideX(xInside, tij, phaseIdx, compIdx); |
| 293 | |||
| 294 |
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230633746 | const Scalar rhoInside = massOrMolarDensity(insideVolVars, referenceSystem, phaseIdx); |
| 295 |
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230633746 | const Scalar rhoOutside = massOrMolarDensity(outsideVolVars, referenceSystem, phaseIdx); |
| 296 | |||
| 297 |
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455368356 | const Scalar rho = getRho(phaseIdx, rhoInside, rhoOutside); |
| 298 | |||
| 299 | 232613346 | componentFlux[compIdx] = rho*tij*(xInside - xOutside); | |
| 300 | if constexpr (!FluidSystem::isTracerFluidSystem()) | ||
| 301 | 218570362 | if (BalanceEqOpts::mainComponentIsBalanced(phaseIdx)) | |
| 302 | 654618396 | componentFlux[FluidSystem::getMainComponent(phaseIdx)] -= componentFlux[compIdx]; | |
| 303 | } | ||
| 304 | |||
| 305 | 220944836 | return componentFlux; | |
| 306 | } | ||
| 307 | |||
| 308 | //! compute the mole/mass fraction at branching facets for network grids | ||
| 309 | 82452 | static Scalar branchingFacetX_(const Problem& problem, | |
| 310 | const Element& element, | ||
| 311 | const FVElementGeometry& fvGeometry, | ||
| 312 | const ElementVolumeVariables& elemVolVars, | ||
| 313 | const ElementFluxVariablesCache& elemFluxVarsCache, | ||
| 314 | const SubControlVolumeFace& scvf, | ||
| 315 | const Scalar insideX, const Scalar insideTi, | ||
| 316 | const int phaseIdx, const int compIdx) | ||
| 317 | { | ||
| 318 | 82452 | Scalar sumTi(insideTi); | |
| 319 | 82452 | Scalar sumXTi(insideTi*insideX); | |
| 320 | |||
| 321 |
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500340 | for (unsigned int i = 0; i < scvf.numOutsideScvs(); ++i) |
| 322 | { | ||
| 323 | 208944 | const auto outsideScvIdx = scvf.outsideScvIdx(i); | |
| 324 | 208944 | const auto& outsideVolVars = elemVolVars[outsideScvIdx]; | |
| 325 | 208944 | const Scalar massOrMoleFractionOutside = massOrMoleFraction(outsideVolVars, referenceSystem, phaseIdx, compIdx); | |
| 326 | 208944 | const auto& flippedScvf = fvGeometry.flipScvf(scvf.index(), i); | |
| 327 | |||
| 328 | 417888 | const Scalar outsideTi = elemFluxVarsCache[flippedScvf].diffusionTij(phaseIdx, compIdx); | |
| 329 | 208944 | sumTi += outsideTi; | |
| 330 | 208944 | sumXTi += outsideTi*massOrMoleFractionOutside; | |
| 331 | } | ||
| 332 | |||
| 333 |
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82452 | return sumTi > 0 ? sumXTi/sumTi : 0; |
| 334 | } | ||
| 335 | |||
| 336 | //! compute the density at branching facets for network grids as arithmetic mean | ||
| 337 | ✗ | static Scalar branchingFacetDensity_(const ElementVolumeVariables& elemVolVars, | |
| 338 | const SubControlVolumeFace& scvf, | ||
| 339 | const int phaseIdx, | ||
| 340 | const Scalar insideRho) | ||
| 341 | { | ||
| 342 | ✗ | Scalar rho(insideRho); | |
| 343 | ✗ | for (unsigned int i = 0; i < scvf.numOutsideScvs(); ++i) | |
| 344 | { | ||
| 345 | ✗ | const auto outsideScvIdx = scvf.outsideScvIdx(i); | |
| 346 | ✗ | const auto& outsideVolVars = elemVolVars[outsideScvIdx]; | |
| 347 | ✗ | const Scalar rhoOutside = massOrMolarDensity(outsideVolVars, referenceSystem, phaseIdx); | |
| 348 | ✗ | rho += rhoOutside; | |
| 349 | } | ||
| 350 | ✗ | return rho/(scvf.numOutsideScvs()+1); | |
| 351 | } | ||
| 352 | |||
| 353 | static constexpr bool isMixedDimensional_ = static_cast<int>(GridView::dimension) < static_cast<int>(GridView::dimensionworld); | ||
| 354 | }; | ||
| 355 | |||
| 356 | } // end namespace Dumux | ||
| 357 | |||
| 358 | #endif | ||
| 359 |