Add connectionMultiPhaseUpwind() free function.

CMakeLists_files.cmake

@@ -35,6 +35,7 @@ list (APPEND MAIN_SOURCE_FILES
   opm/autodiff/GridHelpers.cpp
   opm/autodiff/ImpesTPFAAD.cpp
   opm/autodiff/moduleVersion.cpp
+  opm/autodiff/multiPhaseUpwind.cpp
   opm/autodiff/SimulatorFullyImplicitBlackoilOutput.cpp
   opm/autodiff/SimulatorIncompTwophaseAd.cpp
   opm/autodiff/TransportSolverTwophaseAd.cpp
@@ -188,6 +189,7 @@ list (APPEND PUBLIC_HEADER_FILES
   opm/autodiff/ISTLSolver.hpp
   opm/autodiff/IterationReport.hpp
   opm/autodiff/moduleVersion.hpp
+  opm/autodiff/multiPhaseUpwind.hpp
   opm/autodiff/NewtonIterationBlackoilCPR.hpp
   opm/autodiff/NewtonIterationBlackoilInterface.hpp
   opm/autodiff/NewtonIterationBlackoilInterleaved.hpp

opm/autodiff/multiPhaseUpwind.cpp

@@ -0,0 +1,87 @@
+/*
+  Copyright 2015, 2016 SINTEF ICT, Applied Mathematics.
+  Copyright 2016 Statoil AS.
+
+  This file is part of the Open Porous Media project (OPM).
+
+  OPM 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 3 of the License, or
+  (at your option) any later version.
+
+  OPM 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 OPM.  If not, see <http://www.gnu.org/licenses/>.
+*/
+
+
+#include <opm/autodiff/multiPhaseUpwind.hpp>
+#include <utility>
+
+
+namespace Opm
+{
+
+
+    std::array<double, 3> connectionMultiPhaseUpwind(const std::array<double, 3>& head_diff,
+                                                     const std::array<double, 3>& mob1,
+                                                     const std::array<double, 3>& mob2,
+                                                     const double transmissibility,
+                                                     const double flux)
+    {
+        // Based on the paper "Upstream Differencing for Multiphase Flow in Reservoir Simulation",
+        // by Yann Brenier and Jérôme Jaffré,
+        // SIAM J. Numer. Anal., 28(3), 685–696.
+        // DOI:10.1137/0728036
+        //
+        // Notation is based on this paper, except q -> flux, t -> transmissibility.
+
+        enum { NumPhases = 3 }; // TODO: remove this restriction.
+
+        // Get and sort the g values (also called "weights" in the paper) for this connection.
+        using ValueAndIndex = std::pair<double, int>;
+        std::array<ValueAndIndex, NumPhases> g;
+        for (int phase_idx = 0; phase_idx < NumPhases; ++phase_idx) {
+            g[phase_idx] = ValueAndIndex(head_diff[phase_idx], phase_idx);
+        }
+        std::sort(g.begin(), g.end());
+
+        // Compute theta and r.
+        // Paper notation: subscript l -> ell (for read/searchability)
+        // Note that since we index phases from 0, r is one less than in the paper.
+        std::array<double, NumPhases> theta;
+        int r = -1;
+        for (int ell = 0; ell < NumPhases; ++ell) {
+            theta[ell] = flux;
+            for (int j = 0; j < NumPhases; ++j) {
+                if (j < ell) {
+                    theta[ell] += transmissibility * (g[ell].first - g[j].first) * mob2[g[j].second];
+                }
+                if (j > ell) {
+                    theta[ell] += transmissibility * (g[ell].first - g[j].first) * mob1[g[j].second];
+                }
+            }
+            if (theta[ell] <= 0.0) {
+                r = ell;
+            } else {
+                break; // r is correct, no need to continue
+            }
+        }
+
+        // Set upwind array and return.
+        std::array<double, NumPhases> upwind;
+        for (int ell = 0; ell < NumPhases; ++ell) {
+            const int phase_idx = g[ell].second;
+            upwind[phase_idx] = ell > r ? 1.0 : -1.0;
+        }
+        return upwind;
+
+    }
+
+
+} // namespace Opm
+

opm/autodiff/multiPhaseUpwind.hpp

@@ -0,0 +1,45 @@
+/*
+  Copyright 2015, 2016 SINTEF ICT, Applied Mathematics.
+  Copyright 2016 Statoil AS.
+
+  This file is part of the Open Porous Media project (OPM).
+
+  OPM 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 3 of the License, or
+  (at your option) any later version.
+
+  OPM 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 OPM.  If not, see <http://www.gnu.org/licenses/>.
+*/
+
+#ifndef OPM_MULTIPHASEUPWIND_HEADER_INCLUDED
+#define OPM_MULTIPHASEUPWIND_HEADER_INCLUDED
+
+#include <array>
+
+namespace Opm
+{
+    /// Compute upwind directions for three-phase flow across a connection.
+    ///
+    /// @param[in]  head_diff           head differences by phase
+    /// @param[in]  mob1                phase mobilities for first cell
+    /// @param[in]  mob2                phase mobilities for second cell
+    /// @param[in]  transmissibility    tranmissibility of connection
+    /// @param[in]  flux                total volume flux across connection
+    /// @return array containing, for each phase, 1.0 if flow in the
+    ///         direction of the connection, -1.0 if flow in the opposite
+    ///         direction.
+    std::array<double, 3> connectionMultiPhaseUpwind(const std::array<double, 3>& head_diff,
+                                                     const std::array<double, 3>& mob1,
+                                                     const std::array<double, 3>& mob2,
+                                                     const double transmissibility,
+                                                     const double flux);
+} // namespace Opm
+
+#endif // OPM_MULTIPHASEUPWIND_HEADER_INCLUDED