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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 This file contains the data which is required to calculate | ||
| 11 | * diffusive mass fluxes due to molecular diffusion with Maxwell Stefan | ||
| 12 | */ | ||
| 13 | #ifndef DUMUX_DISCRETIZATION_CC_TPFA_MAXWELL_STEFAN_LAW_HH | ||
| 14 | #define DUMUX_DISCRETIZATION_CC_TPFA_MAXWELL_STEFAN_LAW_HH | ||
| 15 | |||
| 16 | #include <dune/common/fmatrix.hh> | ||
| 17 | #include <dune/common/float_cmp.hh> | ||
| 18 | |||
| 19 | #include <dumux/common/properties.hh> | ||
| 20 | #include <dumux/common/parameters.hh> | ||
| 21 | |||
| 22 | #include <dumux/discretization/method.hh> | ||
| 23 | #include <dumux/discretization/extrusion.hh> | ||
| 24 | #include <dumux/flux/fluxvariablescaching.hh> | ||
| 25 | #include <dumux/flux/referencesystemformulation.hh> | ||
| 26 | #include <dumux/flux/maxwellstefandiffusioncoefficients.hh> | ||
| 27 | |||
| 28 | namespace Dumux { | ||
| 29 | |||
| 30 | // forward declaration | ||
| 31 | template <class TypeTag, class DiscretizationMethod, ReferenceSystemFormulation referenceSystem> | ||
| 32 | class MaxwellStefansLawImplementation; | ||
| 33 | |||
| 34 | /*! | ||
| 35 | * \ingroup CCTpfaFlux | ||
| 36 | * \brief Specialization of Maxwell Stefan's Law for the CCTpfa method. | ||
| 37 | */ | ||
| 38 | template <class TypeTag, ReferenceSystemFormulation referenceSystem> | ||
| 39 | class MaxwellStefansLawImplementation<TypeTag, DiscretizationMethods::CCTpfa, referenceSystem > | ||
| 40 | { | ||
| 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 SubControlVolume = typename GridGeometry::SubControlVolume; | ||
| 46 | using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; | ||
| 47 | using Extrusion = Extrusion_t<GridGeometry>; | ||
| 48 | using GridView = typename GridGeometry::GridView; | ||
| 49 | using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>; | ||
| 50 | using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView; | ||
| 51 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 52 | using GridFluxVariablesCache = GetPropType<TypeTag, Properties::GridFluxVariablesCache>; | ||
| 53 | using ElementFluxVariablesCache = typename GridFluxVariablesCache::LocalView; | ||
| 54 | using FluxVariablesCache = typename GridFluxVariablesCache::FluxVariablesCache; | ||
| 55 | using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>; | ||
| 56 | |||
| 57 | static const int dim = GridView::dimension; | ||
| 58 | static const int dimWorld = GridView::dimensionworld; | ||
| 59 | static const int numPhases = GetPropType<TypeTag, Properties::ModelTraits>::numFluidPhases(); | ||
| 60 | static const int numComponents = GetPropType<TypeTag, Properties::ModelTraits>::numFluidComponents(); | ||
| 61 | |||
| 62 | static_assert(referenceSystem == ReferenceSystemFormulation::massAveraged, "only the mass averaged reference system is supported for the Maxwell-Stefan formulation"); | ||
| 63 | |||
| 64 | |||
| 65 | using ComponentFluxVector = Dune::FieldVector<Scalar, numComponents>; | ||
| 66 | using ReducedComponentVector = Dune::FieldVector<Scalar, numComponents-1>; | ||
| 67 | using ReducedComponentMatrix = Dune::FieldMatrix<Scalar, numComponents-1, numComponents-1>; | ||
| 68 | |||
| 69 | public: | ||
| 70 | using DiscretizationMethod = DiscretizationMethods::CCTpfa; | ||
| 71 | // state the discretization method this implementation belongs to | ||
| 72 | static constexpr DiscretizationMethod discMethod{}; | ||
| 73 | |||
| 74 | //return the reference system | ||
| 75 | static constexpr ReferenceSystemFormulation referenceSystemFormulation() | ||
| 76 | { return referenceSystem; } | ||
| 77 | |||
| 78 | using DiffusionCoefficientsContainer = MaxwellStefanDiffusionCoefficients<Scalar, numPhases, numComponents>; | ||
| 79 | |||
| 80 | //! state the type for the corresponding cache and its filler | ||
| 81 | //! We don't cache anything for this law | ||
| 82 | using Cache = FluxVariablesCaching::EmptyDiffusionCache; | ||
| 83 | using CacheFiller = FluxVariablesCaching::EmptyCacheFiller; | ||
| 84 | |||
| 85 | /*! | ||
| 86 | * \brief Returns the diffusive fluxes of all components within | ||
| 87 | * a fluid phase across the given sub-control volume face. | ||
| 88 | * The computed fluxes are given in kg/s. | ||
| 89 | */ | ||
| 90 | 3058604 | static ComponentFluxVector flux(const Problem& problem, | |
| 91 | const Element& element, | ||
| 92 | const FVElementGeometry& fvGeometry, | ||
| 93 | const ElementVolumeVariables& elemVolVars, | ||
| 94 | const SubControlVolumeFace& scvf, | ||
| 95 | const int phaseIdx, | ||
| 96 | const ElementFluxVariablesCache& elemFluxVarsCache) | ||
| 97 | { | ||
| 98 | //this is to calculate the maxwellStefan diffusion in a multicomponent system. | ||
| 99 | //see: Multicomponent Mass Transfer. R. Taylor u. R. Krishna. J. Wiley & Sons, New York 1993 | ||
| 100 | 3058604 | ComponentFluxVector componentFlux(0.0); | |
| 101 | 3058604 | ReducedComponentVector moleFracInside(0.0); | |
| 102 | 3058604 | ReducedComponentVector moleFracOutside(0.0); | |
| 103 | 3058604 | ReducedComponentVector reducedFlux(0.0); | |
| 104 | 3058604 | ReducedComponentMatrix reducedDiffusionMatrixInside(0.0); | |
| 105 | 3058604 | ReducedComponentMatrix reducedDiffusionMatrixOutside(0.0); | |
| 106 | |||
| 107 | // get inside/outside volume variables | ||
| 108 | 6117208 | const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()]; | |
| 109 | 6117208 | const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()]; | |
| 110 | 3058604 | const auto rhoInside = insideVolVars.density(phaseIdx); | |
| 111 | 3058604 | const auto rhoOutside = outsideVolVars.density(phaseIdx); | |
| 112 | //calculate the mole fraction vectors | ||
| 113 |
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7926232 | for (int compIdx = 0; compIdx < numComponents-1; compIdx++) |
| 114 | { | ||
| 115 | //calculate x_inside | ||
| 116 | 4867628 | const auto xInside = insideVolVars.moleFraction(phaseIdx, compIdx); | |
| 117 | //calculate outside molefraction with the respective transmissibility | ||
| 118 | 4867628 | const auto xOutside = outsideVolVars.moleFraction(phaseIdx, compIdx); | |
| 119 | |||
| 120 | 4867628 | moleFracInside[compIdx] = xInside; | |
| 121 | 8485676 | moleFracOutside[compIdx] = xOutside; | |
| 122 | } | ||
| 123 | |||
| 124 | //we cannot solve that if the matrix is 0 everywhere | ||
| 125 |
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6990388 | if(!(Dune::FloatCmp::eq<Scalar>(insideVolVars.saturation(phaseIdx), 0) || Dune::FloatCmp::eq<Scalar>(outsideVolVars.saturation(phaseIdx), 0))) |
| 126 | { | ||
| 127 |
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2627690 | const auto insideScvIdx = scvf.insideScvIdx(); |
| 128 |
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2627690 | const auto& insideScv = fvGeometry.scv(insideScvIdx); |
| 129 | 2627690 | const Scalar omegai = calculateOmega_(scvf, | |
| 130 | insideScv, | ||
| 131 | insideVolVars.extrusionFactor()); | ||
| 132 | |||
| 133 | //now we have to do the tpfa: J_i = J_j which leads to: tij(xi -xj) = -rho Bi^-1 omegai(x*-xi) with x* = (omegai Bi^-1 + omegaj Bj^-1)^-1 (xi omegai Bi^-1 + xj omegaj Bj^-1) with i inside and j outside | ||
| 134 | 2627690 | reducedDiffusionMatrixInside = setupMSMatrix_(problem, element, fvGeometry, insideVolVars, insideScv, phaseIdx); | |
| 135 | |||
| 136 | //if on boundary | ||
| 137 |
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2627690 | if (scvf.boundary() || scvf.numOutsideScvs() > 1) |
| 138 | { | ||
| 139 | 25410 | moleFracOutside -= moleFracInside; | |
| 140 | 25410 | reducedDiffusionMatrixInside.solve(reducedFlux, moleFracOutside); | |
| 141 | 25410 | reducedFlux *= omegai*rhoInside; | |
| 142 | } | ||
| 143 | else //we need outside cells as well if we are not on the boundary | ||
| 144 | { | ||
| 145 | Scalar omegaj; | ||
| 146 |
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2602280 | const auto outsideScvIdx = scvf.outsideScvIdx(); |
| 147 |
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2602280 | const auto& outsideScv = fvGeometry.scv(outsideScvIdx); |
| 148 | |||
| 149 | 2602280 | reducedDiffusionMatrixOutside = setupMSMatrix_(problem, element, fvGeometry, outsideVolVars, outsideScv, phaseIdx); | |
| 150 | |||
| 151 | if (dim == dimWorld) | ||
| 152 | // assume the normal vector from outside is anti parallel so we save flipping a vector | ||
| 153 | 2602280 | omegaj = -1.0*calculateOmega_(scvf, | |
| 154 | outsideScv, | ||
| 155 | outsideVolVars.extrusionFactor()); | ||
| 156 | else | ||
| 157 | omegaj = calculateOmega_(fvGeometry.flipScvf(scvf.index()), | ||
| 158 | outsideScv, | ||
| 159 | outsideVolVars.extrusionFactor()); | ||
| 160 | |||
| 161 | 2602280 | reducedDiffusionMatrixInside.invert(); | |
| 162 | 2602280 | reducedDiffusionMatrixOutside.invert(); | |
| 163 | 2602280 | reducedDiffusionMatrixInside *= omegai*rhoInside; | |
| 164 | 2602280 | reducedDiffusionMatrixOutside *= omegaj*rhoOutside; | |
| 165 | |||
| 166 | //in the helpervector we store the values for x* | ||
| 167 | 2602280 | ReducedComponentVector helperVector(0.0); | |
| 168 | 2602280 | ReducedComponentVector gradientVectori(0.0); | |
| 169 | 2602280 | ReducedComponentVector gradientVectorj(0.0); | |
| 170 | |||
| 171 | 793256 | reducedDiffusionMatrixInside.mv(moleFracInside, gradientVectori); | |
| 172 | 2602280 | reducedDiffusionMatrixOutside.mv(moleFracOutside, gradientVectorj); | |
| 173 | |||
| 174 | 2602280 | auto gradientVectorij = (gradientVectori + gradientVectorj); | |
| 175 | |||
| 176 | //add the two matrixes to each other | ||
| 177 | 3395536 | reducedDiffusionMatrixOutside += reducedDiffusionMatrixInside; | |
| 178 | |||
| 179 | 2602280 | reducedDiffusionMatrixOutside.solve(helperVector, gradientVectorij); | |
| 180 | |||
| 181 | //Bi^-1 omegai rho(x*-xi) | ||
| 182 | helperVector -=moleFracInside; | ||
| 183 | 1809024 | reducedDiffusionMatrixInside.mv(helperVector, reducedFlux); | |
| 184 | } | ||
| 185 | |||
| 186 | 5255380 | reducedFlux *= -Extrusion::area(fvGeometry, scvf); | |
| 187 |
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7064404 | for (int compIdx = 0; compIdx < numComponents-1; compIdx++) |
| 188 | { | ||
| 189 | 8054762 | componentFlux[compIdx] = reducedFlux[compIdx]; | |
| 190 | 8873428 | componentFlux[numComponents-1] -=reducedFlux[compIdx]; | |
| 191 | } | ||
| 192 | } | ||
| 193 | 3058604 | return componentFlux ; | |
| 194 | } | ||
| 195 | |||
| 196 | private: | ||
| 197 | 5229970 | static Scalar calculateOmega_(const SubControlVolumeFace& scvf, | |
| 198 | const SubControlVolume &scv, | ||
| 199 | const Scalar extrusionFactor) | ||
| 200 | { | ||
| 201 | 5229970 | auto distanceVector = scvf.ipGlobal(); | |
| 202 | 10459940 | distanceVector -= scv.center(); | |
| 203 | distanceVector /= distanceVector.two_norm2(); | ||
| 204 | |||
| 205 | 5229970 | Scalar omega = (distanceVector * scvf.unitOuterNormal()); | |
| 206 | 5229970 | omega *= extrusionFactor; | |
| 207 | |||
| 208 | 5229970 | return omega; | |
| 209 | } | ||
| 210 | |||
| 211 | 5229970 | static ReducedComponentMatrix setupMSMatrix_(const Problem& problem, | |
| 212 | const Element& element, | ||
| 213 | const FVElementGeometry& fvGeometry, | ||
| 214 | const VolumeVariables& volVars, | ||
| 215 | const SubControlVolume& scv, | ||
| 216 | const int phaseIdx) | ||
| 217 | { | ||
| 218 |
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5229970 | ReducedComponentMatrix reducedDiffusionMatrix(0.0); |
| 219 | |||
| 220 | //this is to not divide by 0 if the saturation in 0 and the effectiveDiffusionCoefficient becomes zero due to that | ||
| 221 |
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6948214 | if(Dune::FloatCmp::eq<Scalar>(volVars.saturation(phaseIdx), 0)) |
| 222 | ✗ | return reducedDiffusionMatrix; | |
| 223 | |||
| 224 | 5229970 | const auto avgMolarMass = volVars.averageMolarMass(phaseIdx); | |
| 225 | |||
| 226 |
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14077988 | for (int compIIdx = 0; compIIdx < numComponents-1; compIIdx++) |
| 227 | { | ||
| 228 | 8848018 | const auto xi = volVars.moleFraction(phaseIdx, compIIdx); | |
| 229 | |||
| 230 | 8848018 | const auto Mn = FluidSystem::molarMass(numComponents-1); | |
| 231 | 8848018 | Scalar tin = volVars.effectiveDiffusionCoefficient(phaseIdx, compIIdx, numComponents-1); | |
| 232 | |||
| 233 | // set the entries of the diffusion matrix of the diagonal | ||
| 234 | 16084114 | reducedDiffusionMatrix[compIIdx][compIIdx] += xi*avgMolarMass/(tin*Mn); | |
| 235 | |||
| 236 | // now set the rest of the entries (off-diagonal and additional entries for diagonal) | ||
| 237 |
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33780150 | for (int compJIdx = 0; compJIdx < numComponents; compJIdx++) |
| 238 | { | ||
| 239 | // we don't want to calculate e.g. water in water diffusion | ||
| 240 |
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24932132 | if (compJIdx == compIIdx) |
| 241 | continue; | ||
| 242 | |||
| 243 | 16084114 | const auto xj = volVars.moleFraction(phaseIdx, compJIdx); | |
| 244 | 16084114 | const auto Mi = FluidSystem::molarMass(compIIdx); | |
| 245 | 16084114 | const auto Mj = FluidSystem::molarMass(compJIdx); | |
| 246 | 16084114 | Scalar tij = volVars.effectiveDiffusionCoefficient(phaseIdx, compIIdx, compJIdx); | |
| 247 |
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32168228 | reducedDiffusionMatrix[compIIdx][compIIdx] += xj*avgMolarMass/(tij*Mi); |
| 248 | |||
| 249 |
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14472192 | if (compJIdx < numComponents-1) |
| 250 | 21708288 | reducedDiffusionMatrix[compIIdx][compJIdx] += xi*(avgMolarMass/(tin*Mn) - avgMolarMass/(tij*Mj)); | |
| 251 | } | ||
| 252 | } | ||
| 253 | 1611922 | return reducedDiffusionMatrix; | |
| 254 | } | ||
| 255 | |||
| 256 | }; | ||
| 257 | } // end namespace | ||
| 258 | |||
| 259 | #endif | ||
| 260 |