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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 StaggeredFlux | ||
| 10 | * \brief Specialization of Maxwell Stefan's Law for the Staggered method. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_DISCRETIZATION_STAGGERED_MAXWELL_STEFAN_LAW_HH | ||
| 13 | #define DUMUX_DISCRETIZATION_STAGGERED_MAXWELL_STEFAN_LAW_HH | ||
| 14 | |||
| 15 | #include <dune/common/fmatrix.hh> | ||
| 16 | |||
| 17 | #include <dumux/common/properties.hh> | ||
| 18 | #include <dumux/common/parameters.hh> | ||
| 19 | #include <dumux/discretization/method.hh> | ||
| 20 | #include <dumux/discretization/extrusion.hh> | ||
| 21 | |||
| 22 | #include <dumux/flux/fluxvariablescaching.hh> | ||
| 23 | #include <dumux/flux/referencesystemformulation.hh> | ||
| 24 | #include <dumux/flux/maxwellstefandiffusioncoefficients.hh> | ||
| 25 | |||
| 26 | namespace Dumux { | ||
| 27 | |||
| 28 | // forward declaration | ||
| 29 | template <class TypeTag, class DiscretizationMethod, ReferenceSystemFormulation referenceSystem> | ||
| 30 | class MaxwellStefansLawImplementation; | ||
| 31 | |||
| 32 | /*! | ||
| 33 | * \ingroup StaggeredFlux | ||
| 34 | * \brief Specialization of Maxwell Stefan's Law for the Staggered method. | ||
| 35 | */ | ||
| 36 | template <class TypeTag, ReferenceSystemFormulation referenceSystem> | ||
| 37 | class MaxwellStefansLawImplementation<TypeTag, DiscretizationMethods::Staggered, referenceSystem> | ||
| 38 | { | ||
| 39 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 40 | using Problem = GetPropType<TypeTag, Properties::Problem>; | ||
| 41 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 42 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 43 | using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; | ||
| 44 | using Extrusion = Extrusion_t<GridGeometry>; | ||
| 45 | using GridView = typename GridGeometry::GridView; | ||
| 46 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 47 | using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>; | ||
| 48 | using CellCenterPrimaryVariables = GetPropType<TypeTag, Properties::CellCenterPrimaryVariables>; | ||
| 49 | using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices; | ||
| 50 | using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>; | ||
| 51 | |||
| 52 | using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>; | ||
| 53 | |||
| 54 | static const int numComponents = ModelTraits::numFluidComponents(); | ||
| 55 | static const int numPhases = ModelTraits::numFluidPhases(); | ||
| 56 | static constexpr bool useMoles = getPropValue<TypeTag, Properties::UseMoles>(); | ||
| 57 | |||
| 58 | using ReducedComponentVector = Dune::FieldVector<Scalar, numComponents-1>; | ||
| 59 | using ReducedComponentMatrix = Dune::FieldMatrix<Scalar, numComponents-1, numComponents-1>; | ||
| 60 | |||
| 61 | static_assert(ModelTraits::numFluidPhases() == 1, "Only one phase allowed supported!"); | ||
| 62 | |||
| 63 | static_assert(referenceSystem == ReferenceSystemFormulation::massAveraged, "only the mass averaged reference system is supported for the Maxwell-Stefan formulation"); | ||
| 64 | |||
| 65 | public: | ||
| 66 | using DiscretizationMethod = DiscretizationMethods::Staggered; | ||
| 67 | // state the discretization method this implementation belongs to | ||
| 68 | static constexpr DiscretizationMethod discMethod{}; | ||
| 69 | |||
| 70 | //return the reference system | ||
| 71 | static constexpr ReferenceSystemFormulation referenceSystemFormulation() | ||
| 72 | { return referenceSystem; } | ||
| 73 | |||
| 74 | //! state the type for the corresponding cache and its filler | ||
| 75 | //! We don't cache anything for this law | ||
| 76 | using Cache = FluxVariablesCaching::EmptyDiffusionCache; | ||
| 77 | using CacheFiller = FluxVariablesCaching::EmptyCacheFiller; | ||
| 78 | |||
| 79 | using DiffusionCoefficientsContainer = MaxwellStefanDiffusionCoefficients<Scalar, numPhases, numComponents>; | ||
| 80 | |||
| 81 | /*! | ||
| 82 | * \brief Returns the diffusive fluxes of all components within | ||
| 83 | * a fluid phase across the given sub-control volume face. | ||
| 84 | * The computed fluxes are given in kg/s. | ||
| 85 | */ | ||
| 86 | template<class ElementVolumeVariables> | ||
| 87 | 2574720 | static CellCenterPrimaryVariables flux(const Problem& problem, | |
| 88 | const Element& element, | ||
| 89 | const FVElementGeometry& fvGeometry, | ||
| 90 | const ElementVolumeVariables& elemVolVars, | ||
| 91 | const SubControlVolumeFace& scvf) | ||
| 92 | { | ||
| 93 | //this is to calculate the maxwellStefan diffusion in a multicomponent system. | ||
| 94 | //see: Multicomponent Mass Transfer. R. Taylor u. R. Krishna. J. Wiley & Sons, New York 1993 | ||
| 95 | 2574720 | CellCenterPrimaryVariables componentFlux(0.0); | |
| 96 | 2574720 | ReducedComponentVector moleFracInside(0.0); | |
| 97 | 2574720 | ReducedComponentVector moleFracOutside(0.0); | |
| 98 | 2574720 | ReducedComponentVector reducedFlux(0.0); | |
| 99 | 2574720 | ReducedComponentMatrix reducedDiffusionMatrixInside(0.0); | |
| 100 | 2574720 | ReducedComponentMatrix reducedDiffusionMatrixOutside(0.0); | |
| 101 | |||
| 102 | // get inside/outside volume variables | ||
| 103 | 5149440 | const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()]; | |
| 104 | 5149440 | const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()]; | |
| 105 | 2574720 | const auto rhoInside = insideVolVars.density(); | |
| 106 | 2574720 | const auto rhoOutside = outsideVolVars.density(); | |
| 107 | |||
| 108 | //to implement outflow boundaries correctly we need to loop over all components but the main component as only for the transported ones we implement the outflow boundary. diffusion then is 0. | ||
| 109 |
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9309368 | for(int compIdx = 0; compIdx < numComponents; ++compIdx) |
| 110 | { | ||
| 111 |
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6762584 | if(compIdx == FluidSystem::getMainComponent(0)) |
| 112 | continue; | ||
| 113 | |||
| 114 | // get equation index | ||
| 115 | 4187864 | const auto eqIdx = Indices::conti0EqIdx + compIdx; | |
| 116 |
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4187864 | if(scvf.boundary()) |
| 117 | { | ||
| 118 | 174120 | const auto bcTypes = problem.boundaryTypes(element, scvf); | |
| 119 |
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348240 | if((bcTypes.isOutflow(eqIdx)) || (bcTypes.isSymmetry())) |
| 120 | 27936 | return componentFlux; | |
| 121 | } | ||
| 122 | } | ||
| 123 | |||
| 124 | //calculate the mole fraction vectors | ||
| 125 |
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6706712 | for (int compIdx = 0; compIdx < numComponents-1; compIdx++) |
| 126 | { | ||
| 127 | //calculate x_inside | ||
| 128 | 4159928 | const auto xInside = insideVolVars.moleFraction(compIdx); | |
| 129 | //calculate outside molefraction with the respective transmissibility | ||
| 130 | 4159928 | const auto xOutside = outsideVolVars.moleFraction(compIdx); | |
| 131 | |||
| 132 | 4159928 | moleFracInside[compIdx] = xInside; | |
| 133 | 7386216 | moleFracOutside[compIdx] = xOutside; | |
| 134 | } | ||
| 135 | |||
| 136 | //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 | ||
| 137 | 2546784 | reducedDiffusionMatrixInside = setupMSMatrix_(problem, fvGeometry, insideVolVars, scvf); | |
| 138 | |||
| 139 | 2546784 | reducedDiffusionMatrixOutside = setupMSMatrix_(problem, fvGeometry, outsideVolVars, scvf); | |
| 140 | |||
| 141 | 2546784 | const auto insideScvIdx = scvf.insideScvIdx(); | |
| 142 | 2546784 | const auto& insideScv = fvGeometry.scv(insideScvIdx); | |
| 143 | 2546784 | const auto outsideScvIdx = scvf.outsideScvIdx(); | |
| 144 | 2546784 | const auto& outsideScv = fvGeometry.scv(outsideScvIdx); | |
| 145 | |||
| 146 | 10187136 | const Scalar insideDistance = (insideScv.dofPosition() - scvf.ipGlobal()).two_norm(); | |
| 147 | |||
| 148 | 5093568 | const Scalar omegai = calculateOmega_(insideDistance, insideVolVars.extrusionFactor()); | |
| 149 | |||
| 150 | //if on boundary | ||
| 151 | 2546784 | if (scvf.boundary()) | |
| 152 | { | ||
| 153 | 89712 | moleFracOutside -= moleFracInside; | |
| 154 | 89712 | reducedDiffusionMatrixInside.solve(reducedFlux, moleFracOutside); | |
| 155 | 89712 | reducedFlux *= omegai*rhoInside; | |
| 156 | } | ||
| 157 | else | ||
| 158 | { | ||
| 159 | 9828288 | const Scalar outsideDistance = (outsideScv.dofPosition() - scvf.ipGlobal()).two_norm(); | |
| 160 | 4914144 | const Scalar omegaj = calculateOmega_(outsideDistance, outsideVolVars.extrusionFactor()); | |
| 161 | |||
| 162 | 4914144 | reducedDiffusionMatrixInside.invert(); | |
| 163 | 2457072 | reducedDiffusionMatrixOutside.invert(); | |
| 164 | 2457072 | reducedDiffusionMatrixInside *= omegai*rhoInside; | |
| 165 | 2457072 | reducedDiffusionMatrixOutside *= omegaj*rhoOutside; | |
| 166 | |||
| 167 | //in the helpervector we store the values for x* | ||
| 168 | 2457072 | ReducedComponentVector helperVector(0.0); | |
| 169 | 2457072 | ReducedComponentVector gradientVectori(0.0); | |
| 170 | 2457072 | ReducedComponentVector gradientVectorj(0.0); | |
| 171 | |||
| 172 | 900400 | reducedDiffusionMatrixInside.mv(moleFracInside, gradientVectori); | |
| 173 | 2457072 | reducedDiffusionMatrixOutside.mv(moleFracOutside, gradientVectorj); | |
| 174 | |||
| 175 | 2457072 | auto gradientVectorij = (gradientVectori + gradientVectorj); | |
| 176 | |||
| 177 | //add the two matrixes to each other | ||
| 178 | 3357472 | reducedDiffusionMatrixOutside += reducedDiffusionMatrixInside; | |
| 179 | |||
| 180 | 2457072 | reducedDiffusionMatrixOutside.solve(helperVector, gradientVectorij); | |
| 181 | |||
| 182 | //Bi^-1 omegai rho(x*-xi) | ||
| 183 | helperVector -=moleFracInside; | ||
| 184 | 1556672 | reducedDiffusionMatrixInside.mv(helperVector, reducedFlux); | |
| 185 | } | ||
| 186 | |||
| 187 | 5093568 | reducedFlux *= -Extrusion::area(fvGeometry, scvf); | |
| 188 | |||
| 189 |
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6706712 | for (int compIdx = 0; compIdx < numComponents-1; compIdx++) |
| 190 | { | ||
| 191 | 7386216 | componentFlux[compIdx] = reducedFlux[compIdx]; | |
| 192 | 11546144 | componentFlux[numComponents-1] -= reducedFlux[compIdx]; | |
| 193 | } | ||
| 194 | |||
| 195 | 933640 | return componentFlux ; | |
| 196 | } | ||
| 197 | |||
| 198 | private: | ||
| 199 | static Scalar calculateOmega_(const Scalar distance, | ||
| 200 | const Scalar extrusionFactor) | ||
| 201 | { | ||
| 202 | 5003856 | Scalar omega = 1/distance; | |
| 203 |
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5003856 | omega *= extrusionFactor; |
| 204 | |||
| 205 | return omega; | ||
| 206 | } | ||
| 207 | |||
| 208 | 5093568 | static ReducedComponentMatrix setupMSMatrix_(const Problem& problem, | |
| 209 | const FVElementGeometry& fvGeometry, | ||
| 210 | const VolumeVariables& volVars, | ||
| 211 | const SubControlVolumeFace& scvf) | ||
| 212 | { | ||
| 213 | 5093568 | ReducedComponentMatrix reducedDiffusionMatrix(0.0); | |
| 214 | |||
| 215 |
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13413424 | for (int compIIdx = 0; compIIdx < numComponents-1; compIIdx++) |
| 216 | { | ||
| 217 | 8319856 | const auto xi = volVars.moleFraction(compIIdx); | |
| 218 | 8319856 | const auto avgMolarMass = volVars.averageMolarMass(0); | |
| 219 | 8319856 | const auto Mn = FluidSystem::molarMass(numComponents-1); | |
| 220 | 16639712 | const Scalar tin = getEffectiveDiffusionCoefficient_(volVars, compIIdx, numComponents-1); | |
| 221 | |||
| 222 | // set the entries of the diffusion matrix of the diagonal | ||
| 223 | 10187136 | reducedDiffusionMatrix[compIIdx][compIIdx] += xi*avgMolarMass/(tin*Mn); | |
| 224 | |||
| 225 |
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31412144 | for (int compJIdx = 0; compJIdx < numComponents; compJIdx++) |
| 226 | { | ||
| 227 | // we don't want to calculate e.g. water in water diffusion | ||
| 228 |
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23092288 | if (compJIdx == compIIdx) |
| 229 | continue; | ||
| 230 | |||
| 231 | 14772432 | const auto xj = volVars.moleFraction(compJIdx); | |
| 232 | 14772432 | const auto Mi = FluidSystem::molarMass(compIIdx); | |
| 233 | 14772432 | const auto Mj = FluidSystem::molarMass(compJIdx); | |
| 234 | 29544864 | const Scalar tij = getEffectiveDiffusionCoefficient_(volVars, compIIdx, compJIdx); | |
| 235 |
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14772432 | reducedDiffusionMatrix[compIIdx][compIIdx] += xj*avgMolarMass/(tij*Mi); |
| 236 |
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12905152 | if (compJIdx < numComponents-1) |
| 237 | 19357728 | reducedDiffusionMatrix[compIIdx][compJIdx] += xi*(avgMolarMass/(tin*Mn) - avgMolarMass/(tij*Mj)); | |
| 238 | } | ||
| 239 | } | ||
| 240 | 5093568 | return reducedDiffusionMatrix; | |
| 241 | } | ||
| 242 | |||
| 243 | static Scalar getEffectiveDiffusionCoefficient_(const VolumeVariables& volVars, const int phaseIdx, const int compIdx) | ||
| 244 | { | ||
| 245 |
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23092288 | return volVars.effectiveDiffusionCoefficient(phaseIdx, FluidSystem::getMainComponent(phaseIdx), compIdx); |
| 246 | } | ||
| 247 | }; | ||
| 248 | } // end namespace | ||
| 249 | |||
| 250 | #endif | ||
| 251 |