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88 lines
3.2 KiB
C++
88 lines
3.2 KiB
C++
/*
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Copyright 2015, 2016 SINTEF ICT, Applied Mathematics.
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Copyright 2016 Statoil AS.
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This file is part of the Open Porous Media project (OPM).
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OPM is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OPM is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with OPM. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include <opm/autodiff/multiPhaseUpwind.hpp>
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#include <utility>
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namespace Opm
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{
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std::array<double, 3> connectionMultiPhaseUpwind(const std::array<double, 3>& head_diff,
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const std::array<double, 3>& mob1,
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const std::array<double, 3>& mob2,
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const double transmissibility,
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const double flux)
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{
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// Based on the paper "Upstream Differencing for Multiphase Flow in Reservoir Simulation",
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// by Yann Brenier and Jérôme Jaffré,
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// SIAM J. Numer. Anal., 28(3), 685–696.
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// DOI:10.1137/0728036
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//
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// Notation is based on this paper, except q -> flux, t -> transmissibility.
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enum { NumPhases = 3 }; // TODO: remove this restriction.
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// Get and sort the g values (also called "weights" in the paper) for this connection.
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using ValueAndIndex = std::pair<double, int>;
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std::array<ValueAndIndex, NumPhases> g;
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for (int phase_idx = 0; phase_idx < NumPhases; ++phase_idx) {
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g[phase_idx] = ValueAndIndex(head_diff[phase_idx], phase_idx);
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}
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std::sort(g.begin(), g.end());
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// Compute theta and r.
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// Paper notation: subscript l -> ell (for read/searchability)
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// Note that since we index phases from 0, r is one less than in the paper.
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std::array<double, NumPhases> theta;
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int r = -1;
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for (int ell = 0; ell < NumPhases; ++ell) {
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theta[ell] = flux;
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for (int j = 0; j < NumPhases; ++j) {
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if (j < ell) {
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theta[ell] += transmissibility * (g[ell].first - g[j].first) * mob2[g[j].second];
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}
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if (j > ell) {
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theta[ell] += transmissibility * (g[ell].first - g[j].first) * mob1[g[j].second];
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}
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}
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if (theta[ell] <= 0.0) {
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r = ell;
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} else {
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break; // r is correct, no need to continue
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}
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}
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// Set upwind array and return.
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std::array<double, NumPhases> upwind;
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for (int ell = 0; ell < NumPhases; ++ell) {
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const int phase_idx = g[ell].second;
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upwind[phase_idx] = ell > r ? 1.0 : -1.0;
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}
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return upwind;
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}
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} // namespace Opm
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