mpncmodel.hh 8.27 KB
 Bernd Flemisch committed Nov 27, 2012 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- // vi: set et ts=4 sw=4 sts=4: /***************************************************************************** * See the file COPYING for full copying permissions. * * * * This program is free software: you can redistribute it and/or modify * * it under the terms of the GNU General Public License as published by * * the Free Software Foundation, either version 2 of the License, or * * (at your option) any later version. * * * * This program is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * * GNU General Public License for more details. * * * * You should have received a copy of the GNU General Public License * * along with this program. If not, see . * *****************************************************************************/  Thomas Fetzer committed Mar 04, 2013 19 20 21 22 23 24 25 /*! * \file * \brief A fully implicit model for M-phase, N-component flow using * vertex centered finite volumes. * */  Bernd Flemisch committed Nov 27, 2012 26 27 28 29 30 31 #ifndef DUMUX_MPNC_MODEL_HH #define DUMUX_MPNC_MODEL_HH #include "mpncproperties.hh" #include "mpncvtkwriter.hh"  32 #include  Bernd Flemisch committed Nov 27, 2012 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47  namespace Dumux { /*! * \ingroup MPNCModel * \brief A fully implicit model for M-phase, N-component flow using * vertex centered finite volumes. * * This model implements a \f$M\f$-phase flow of a fluid mixture * composed of \f$N\f$ chemical species. The phases are denoted by * lower index \f$\alpha \in \{ 1, \dots, M \}\f$. All fluid phases * are mixtures of \f$N \geq M - 1\f$ chemical species which are * denoted by the upper index \f$\kappa \in \{ 1, \dots, N \} \f$. * * The momentum approximation can be selected via "BaseFluxVariables":  Bernd Flemisch committed Nov 29, 2012 48  * Darcy (ImplicitDarcyFluxVariables) and Forchheimer (ImplicitForchheimerFluxVariables)  Bernd Flemisch committed Nov 27, 2012 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138  * relations are available for all Box models. * * By inserting this into the equations for the conservation of the * mass of each component, one gets one mass-continuity equation for * each component \f$\kappa\f$ * \f[ \sum_{\kappa} \left( \phi \frac{\partial \left(\varrho_\alpha x_\alpha^\kappa S_\alpha\right)}{\partial t} + \mathrm{div}\; \left\{ v_\alpha \frac{\varrho_\alpha}{\overline M_\alpha} x_\alpha^\kappa \right\} \right) = q^\kappa \f] * with \f$\overline M_\alpha\f$ being the average molar mass of the * phase \f$\alpha\f$: \f[ \overline M_\alpha = \sum_\kappa M^\kappa * \; x_\alpha^\kappa \f] * * For the missing \f$M\f$ model assumptions, the model assumes that * if a fluid phase is not present, the sum of the mole fractions of * this fluid phase is smaller than \f$1\f$, i.e. * \f[ * \forall \alpha: S_\alpha = 0 \implies \sum_\kappa x_\alpha^\kappa \leq 1 * \f] * * Also, if a fluid phase may be present at a given spatial location * its saturation must be positive: * \f[ \forall \alpha: \sum_\kappa x_\alpha^\kappa = 1 \implies S_\alpha \geq 0 \f] * * Since at any given spatial location, a phase is always either * present or not present, one of the strict equalities on the * right hand side is always true, i.e. * \f[ \forall \alpha: S_\alpha \left( \sum_\kappa x_\alpha^\kappa - 1 \right) = 0 \f] * always holds. * * These three equations constitute a non-linear complementarity * problem, which can be solved using so-called non-linear * complementarity functions \f$\Phi(a, b)\f$ which have the property * \f[\Phi(a,b) = 0 \iff a \geq0 \land b \geq0 \land a \cdot b = 0 \f] * * Several non-linear complementarity functions have been suggested, * e.g. the Fischer-Burmeister function * \f[ \Phi(a,b) = a + b - \sqrt{a^2 + b^2} \;. \f] * This model uses * \f[ \Phi(a,b) = \min \{a, b \}\;, \f] * because of its piecewise linearity. * * These equations are then discretized using a fully-implicit vertex * centered finite volume scheme (often known as 'box'-scheme) for * spatial discretization and the implicit Euler method as temporal * discretization. * * The model assumes local thermodynamic equilibrium and uses the * following primary variables: * - The component fugacities \f$f^1, \dots, f^{N}\f$ * - The pressure of the first phase \f$p_1\f$ * - The saturations of the first \f$M-1\f$ phases \f$S_1, \dots, S_{M-1}\f$ * - Temperature \f$T\f$ if the energy equation is enabled */ template class MPNCModel : public GET_PROP_TYPE(TypeTag, BaseModel) { typedef typename GET_PROP_TYPE(TypeTag, BaseModel) ParentType; typedef typename GET_PROP_TYPE(TypeTag, Problem) Problem; typedef typename GET_PROP_TYPE(TypeTag, GridView) GridView; typedef typename GridView::template Codim<0>::Entity Element; typedef typename GridView::template Codim<0>::Iterator ElementIterator; typedef typename GET_PROP_TYPE(TypeTag, PrimaryVariables) PrimaryVariables; typedef typename GET_PROP_TYPE(TypeTag, SolutionVector) SolutionVector; typedef Dumux::MPNCVtkWriter MPNCVtkWriter; enum {enableEnergy = GET_PROP_VALUE(TypeTag, EnableEnergy)}; enum {enableDiffusion = GET_PROP_VALUE(TypeTag, EnableDiffusion)}; enum {enableKinetic = GET_PROP_VALUE(TypeTag, EnableKinetic)}; enum {enableKineticEnergy = GET_PROP_VALUE(TypeTag, EnableKineticEnergy)}; enum {enableSmoothUpwinding = GET_PROP_VALUE(TypeTag, ImplicitEnableSmoothUpwinding)}; enum {enablePartialReassemble = GET_PROP_VALUE(TypeTag, ImplicitEnablePartialReassemble)}; enum {enableJacobianRecycling = GET_PROP_VALUE(TypeTag, ImplicitEnableJacobianRecycling)}; enum {numDiffMethod = GET_PROP_VALUE(TypeTag, ImplicitNumericDifferenceMethod)}; enum {numPhases = GET_PROP_VALUE(TypeTag, NumPhases)}; enum {numComponents = GET_PROP_VALUE(TypeTag, NumComponents)}; enum {numEq = GET_PROP_VALUE(TypeTag, NumEq)}; public: void init(Problem &problem) { ParentType::init(problem);  Bernd Flemisch committed Feb 05, 2013 139  vtkWriter_ = Dune::make_shared(problem);  Bernd Flemisch committed Nov 27, 2012 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184  if (this->gridView_().comm().rank() == 0) std::cout << "Initializing M-phase N-component model: \n" << " phases: " << numPhases << "\n" << " components: " << numComponents << "\n" << " equations: " << numEq << "\n" << " kinetic mass transfer: " << enableKinetic<< "\n" << " kinetic energy transfer: " << enableKineticEnergy<< "\n" << " diffusion: " << enableDiffusion << "\n" << " energy equation: " << enableEnergy << "\n" << " smooth upwinding: " << enableSmoothUpwinding << "\n" << " partial jacobian reassembly: " << enablePartialReassemble << "\n" << " numeric differentiation method: " << numDiffMethod << " (-1: backward, 0: central, +1 forward)\n" << " jacobian recycling: " << enableJacobianRecycling << "\n"; } /*! * \brief Compute the total storage inside one phase of all * conservation quantities. */ void globalPhaseStorage(PrimaryVariables &phaseStorage, const unsigned int phaseIdx) { phaseStorage = 0; ElementIterator elemIt = this->gridView_().template begin<0>(); const ElementIterator elemEndIt = this->gridView_().template end<0>(); for (; elemIt != elemEndIt; ++elemIt) { this->localResidual().addPhaseStorage(phaseStorage, *elemIt, phaseIdx); } if (this->gridView_().comm().size() > 1) phaseStorage = this->gridView_().comm().sum(phaseStorage); } /*! * \brief Add the result of the current timestep to the VTK output. */ template void addOutputVtkFields(const SolutionVector &sol, MultiWriter &writer) { vtkWriter_->addCurrentSolution(writer); }  Bernd Flemisch committed Feb 05, 2013 185  Dune::shared_ptr vtkWriter_;  Bernd Flemisch committed Nov 27, 2012 186 187 188 189 190 191 192 }; } #include "mpncpropertydefaults.hh" #endif