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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 molar fluxes due to molecular diffusion with Maxwell Stefan | ||
| 12 | */ | ||
| 13 | #ifndef DUMUX_DISCRETIZATION_BOX_MAXWELL_STEFAN_LAW_HH | ||
| 14 | #define DUMUX_DISCRETIZATION_BOX_MAXWELL_STEFAN_LAW_HH | ||
| 15 | |||
| 16 | #include <dune/common/float_cmp.hh> | ||
| 17 | #include <dune/common/fmatrix.hh> | ||
| 18 | |||
| 19 | #include <dumux/common/properties.hh> | ||
| 20 | #include <dumux/common/parameters.hh> | ||
| 21 | #include <dumux/discretization/method.hh> | ||
| 22 | #include <dumux/discretization/extrusion.hh> | ||
| 23 | |||
| 24 | #include <dumux/flux/maxwellstefandiffusioncoefficients.hh> | ||
| 25 | #include <dumux/flux/fluxvariablescaching.hh> | ||
| 26 | #include <dumux/flux/referencesystemformulation.hh> | ||
| 27 | #include <dumux/flux/facetensoraverage.hh> | ||
| 28 | |||
| 29 | namespace Dumux { | ||
| 30 | |||
| 31 | // forward declaration | ||
| 32 | template <class TypeTag, class DiscretizationMethod, ReferenceSystemFormulation referenceSystem> | ||
| 33 | class MaxwellStefansLawImplementation; | ||
| 34 | |||
| 35 | /*! | ||
| 36 | * \ingroup BoxFlux | ||
| 37 | * \brief Specialization of Maxwell Stefan's Law for the Box method. | ||
| 38 | */ | ||
| 39 | template <class TypeTag, ReferenceSystemFormulation referenceSystem> | ||
| 40 | class MaxwellStefansLawImplementation<TypeTag, DiscretizationMethods::Box, referenceSystem> | ||
| 41 | { | ||
| 42 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 43 | using Problem = GetPropType<TypeTag, Properties::Problem>; | ||
| 44 | using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>; | ||
| 45 | using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>; | ||
| 46 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 47 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 48 | using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace; | ||
| 49 | using Extrusion = Extrusion_t<GridGeometry>; | ||
| 50 | using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView; | ||
| 51 | using ElementFluxVariablesCache = typename GetPropType<TypeTag, Properties::GridFluxVariablesCache>::LocalView; | ||
| 52 | using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView; | ||
| 53 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 54 | |||
| 55 | static constexpr auto numFluidPhases = GetPropType<TypeTag, Properties::ModelTraits>::numFluidPhases(); | ||
| 56 | static constexpr auto numComponents = GetPropType<TypeTag, Properties::ModelTraits>::numFluidComponents(); | ||
| 57 | |||
| 58 | using ComponentFluxVector = Dune::FieldVector<Scalar, numComponents>; | ||
| 59 | using ReducedComponentVector = Dune::FieldVector<Scalar, numComponents-1>; | ||
| 60 | using ReducedComponentMatrix = Dune::FieldMatrix<Scalar, numComponents-1, numComponents-1>; | ||
| 61 | |||
| 62 | static_assert(referenceSystem == ReferenceSystemFormulation::massAveraged, "only the mass averaged reference system is supported for the Maxwell-Stefan formulation"); | ||
| 63 | |||
| 64 | public: | ||
| 65 | using DiffusionCoefficientsContainer = MaxwellStefanDiffusionCoefficients<Scalar, numFluidPhases, numComponents>; | ||
| 66 | |||
| 67 | //return the reference system | ||
| 68 | static constexpr ReferenceSystemFormulation referenceSystemFormulation() | ||
| 69 | { return referenceSystem; } | ||
| 70 | |||
| 71 | /*! | ||
| 72 | * \brief Returns the diffusive fluxes of all components within | ||
| 73 | * a fluid phase across the given sub-control volume face. | ||
| 74 | * The computed fluxes are given in kg/s. | ||
| 75 | */ | ||
| 76 | 764400 | static ComponentFluxVector flux(const Problem& problem, | |
| 77 | const Element& element, | ||
| 78 | const FVElementGeometry& fvGeometry, | ||
| 79 | const ElementVolumeVariables& elemVolVars, | ||
| 80 | const SubControlVolumeFace& scvf, | ||
| 81 | const int phaseIdx, | ||
| 82 | const ElementFluxVariablesCache& elemFluxVarsCache) | ||
| 83 | { | ||
| 84 | //this is to calculate the maxwellStefan diffusion in a multicomponent system. | ||
| 85 | //see: Multicomponent Mass Transfer. R. Taylor u. R. Krishna. J. Wiley & Sons, New York 1993 | ||
| 86 | 764400 | ComponentFluxVector componentFlux(0.0); | |
| 87 | 764400 | ReducedComponentMatrix reducedDiffusionMatrix(0.0); | |
| 88 | 764400 | ReducedComponentVector reducedFlux(0.0); | |
| 89 | 764400 | ComponentFluxVector moleFrac(0.0); | |
| 90 | 764400 | ReducedComponentVector normalX(0.0); | |
| 91 | |||
| 92 | // evaluate gradX at integration point and interpolate density | ||
| 93 | 764400 | const auto& fluxVarsCache = elemFluxVarsCache[scvf]; | |
| 94 | 764400 | const auto& shapeValues = fluxVarsCache.shapeValues(); | |
| 95 | |||
| 96 | 764400 | Scalar rho(0.0); | |
| 97 | 764400 | Scalar avgMolarMass(0.0); | |
| 98 |
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4586400 | for (auto&& scv : scvs(fvGeometry)) |
| 99 | { | ||
| 100 | 3057600 | const auto& volVars = elemVolVars[scv]; | |
| 101 | |||
| 102 | // density interpolation | ||
| 103 | 6115200 | rho += volVars.density(phaseIdx)*shapeValues[scv.indexInElement()][0]; | |
| 104 | //average molar mass interpolation | ||
| 105 | 3057600 | avgMolarMass += volVars.averageMolarMass(phaseIdx)*shapeValues[scv.indexInElement()][0]; | |
| 106 | //interpolate the mole fraction for the diffusion matrix | ||
| 107 |
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12230400 | for (int compIdx = 0; compIdx < numComponents; compIdx++) |
| 108 | { | ||
| 109 | 27518400 | moleFrac[compIdx] += volVars.moleFraction(phaseIdx, compIdx)*shapeValues[scv.indexInElement()][0]; | |
| 110 | } | ||
| 111 | } | ||
| 112 | |||
| 113 | 764400 | reducedDiffusionMatrix = setupMSMatrix_(problem, element, fvGeometry, elemVolVars, scvf, phaseIdx, moleFrac, avgMolarMass); | |
| 114 | |||
| 115 |
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2293200 | for (int compIdx = 0; compIdx < numComponents-1; compIdx++) |
| 116 | { | ||
| 117 | 1528800 | Dune::FieldVector<Scalar, GridView::dimensionworld> gradX(0.0); | |
| 118 |
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15288000 | for (auto&& scv : scvs(fvGeometry)) |
| 119 | { | ||
| 120 | 6115200 | const auto& volVars = elemVolVars[scv]; | |
| 121 | |||
| 122 | // the mole/mass fraction gradient | ||
| 123 | 24460800 | gradX.axpy(volVars.moleFraction(phaseIdx, compIdx), fluxVarsCache.gradN(scv.indexInElement())); | |
| 124 | } | ||
| 125 | |||
| 126 | 6115200 | normalX[compIdx] = gradX *scvf.unitOuterNormal(); | |
| 127 | } | ||
| 128 | 764400 | reducedDiffusionMatrix.solve(reducedFlux,normalX); | |
| 129 | 1528800 | reducedFlux *= -1.0*rho*Extrusion::area(fvGeometry, scvf); | |
| 130 | |||
| 131 |
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2293200 | for (int compIdx = 0; compIdx < numComponents-1; compIdx++) |
| 132 | { | ||
| 133 | 3057600 | componentFlux[compIdx] = reducedFlux[compIdx]; | |
| 134 | 4586400 | componentFlux[numComponents-1] -= reducedFlux[compIdx]; | |
| 135 | } | ||
| 136 | 764400 | return componentFlux ; | |
| 137 | } | ||
| 138 | |||
| 139 | private: | ||
| 140 | |||
| 141 | 764400 | static ReducedComponentMatrix setupMSMatrix_(const Problem& problem, | |
| 142 | const Element& element, | ||
| 143 | const FVElementGeometry& fvGeometry, | ||
| 144 | const ElementVolumeVariables& elemVolVars, | ||
| 145 | const SubControlVolumeFace& scvf, | ||
| 146 | const int phaseIdx, | ||
| 147 | const ComponentFluxVector moleFrac, | ||
| 148 | const Scalar avgMolarMass) | ||
| 149 | { | ||
| 150 | 764400 | ReducedComponentMatrix reducedDiffusionMatrix(0.0); | |
| 151 | |||
| 152 |
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1528800 | const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()]; |
| 153 |
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764400 | const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()]; |
| 154 | |||
| 155 | //this is to not divide by 0 if the saturation in 0 and the effectiveDiffusionCoefficient becomes zero due to that | ||
| 156 | 2293200 | if(Dune::FloatCmp::eq<Scalar>(insideVolVars.saturation(phaseIdx), 0) || Dune::FloatCmp::eq<Scalar>(outsideVolVars.saturation(phaseIdx), 0)) | |
| 157 | return reducedDiffusionMatrix; | ||
| 158 | |||
| 159 |
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2293200 | for (int compIIdx = 0; compIIdx < numComponents-1; compIIdx++) |
| 160 | { | ||
| 161 | //calculate diffusivity for i,numComponents | ||
| 162 | 1528800 | const auto xi = moleFrac[compIIdx]; | |
| 163 | 1528800 | const auto Mn = FluidSystem::molarMass(numComponents-1); | |
| 164 | |||
| 165 | 1528800 | auto tinInside = insideVolVars.effectiveDiffusionCoefficient(phaseIdx, compIIdx, numComponents-1); | |
| 166 | 1528800 | auto tinOutside = outsideVolVars.effectiveDiffusionCoefficient(phaseIdx, compIIdx, numComponents-1); | |
| 167 | |||
| 168 | // scale by extrusion factor | ||
| 169 | 1528800 | tinInside *= insideVolVars.extrusionFactor(); | |
| 170 | 1528800 | tinOutside *= outsideVolVars.extrusionFactor(); | |
| 171 | |||
| 172 | // the resulting averaged diffusion tensor | ||
| 173 |
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3057600 | const auto tin = faceTensorAverage(tinInside, tinOutside, scvf.unitOuterNormal()); |
| 174 | |||
| 175 | // begin with the entries of the diffusion matrix of the diagonal | ||
| 176 | 3057600 | reducedDiffusionMatrix[compIIdx][compIIdx] += xi*avgMolarMass/(tin*Mn); | |
| 177 | |||
| 178 | // now set the rest of the entries (off-diagonal and additional entries for diagonal) | ||
| 179 |
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6115200 | for (int compJIdx = 0; compJIdx < numComponents; compJIdx++) |
| 180 | { | ||
| 181 | //we don't want to calculate e.g. water in water diffusion | ||
| 182 |
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4586400 | if (compIIdx == compJIdx) |
| 183 | continue; | ||
| 184 | |||
| 185 | //calculate diffusivity for compIIdx, compJIdx | ||
| 186 | 3057600 | const auto xj = moleFrac[compJIdx]; | |
| 187 | 3057600 | const auto Mi = FluidSystem::molarMass(compIIdx); | |
| 188 | 3057600 | const auto Mj = FluidSystem::molarMass(compJIdx); | |
| 189 | |||
| 190 | // effective diffusion tensors | ||
| 191 | 3057600 | auto tijInside = insideVolVars.effectiveDiffusionCoefficient(phaseIdx, compIIdx, compJIdx); | |
| 192 | 3057600 | auto tijOutside = outsideVolVars.effectiveDiffusionCoefficient(phaseIdx, compIIdx, compJIdx); | |
| 193 | |||
| 194 | // scale by extrusion factor | ||
| 195 | 3057600 | tijInside *= insideVolVars.extrusionFactor(); | |
| 196 | 3057600 | tijOutside *= outsideVolVars.extrusionFactor(); | |
| 197 | |||
| 198 | // the resulting averaged diffusion tensor | ||
| 199 |
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3057600 | const auto tij = faceTensorAverage(tijInside, tijOutside, scvf.unitOuterNormal()); |
| 200 | |||
| 201 |
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6115200 | reducedDiffusionMatrix[compIIdx][compIIdx] += xj*avgMolarMass/(tij*Mi); |
| 202 |
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3057600 | if (compJIdx < numComponents-1) |
| 203 | 4586400 | reducedDiffusionMatrix[compIIdx][compJIdx] +=xi*(avgMolarMass/(tin*Mn) - avgMolarMass/(tij*Mj)); | |
| 204 | } | ||
| 205 | } | ||
| 206 | return reducedDiffusionMatrix; | ||
| 207 | } | ||
| 208 | |||
| 209 | }; | ||
| 210 | } // end namespace Dumux | ||
| 211 | |||
| 212 | #endif | ||
| 213 |