Added limiter for DG1, parameter 'use_limiter'.

The limiter is experimental and unfinished, untested work in progress.
Limiter is therefore inactive by default.

Also fixed a minor bug: use_cvi_ was not initialized.

examples/compute_tof_from_files.cpp

@@ -124,10 +124,12 @@ main(int argc, char** argv)
     bool use_dg = param.getDefault("use_dg", false);
     int dg_degree = -1;
     bool use_cvi = false;
+    bool use_limiter = false;
     bool use_multidim_upwind = false;
     if (use_dg) {
         dg_degree = param.getDefault("dg_degree", 0);
         use_cvi = param.getDefault("use_cvi", false);
+        use_limiter = param.getDefault("use_limiter", false);
     } else {
         use_multidim_upwind = param.getDefault("use_multidim_upwind", false);
     }
@@ -157,7 +159,7 @@ main(int argc, char** argv)
     transport_timer.start();
     std::vector<double> tof;
     if (use_dg) {
-        Opm::TransportModelTracerTofDiscGal tofsolver(grid, use_cvi);
+        Opm::TransportModelTracerTofDiscGal tofsolver(grid, use_cvi, use_limiter);
         tofsolver.solveTof(&flux[0], &porevol[0], &src[0], dg_degree, tof);
     } else {
         Opm::TransportModelTracerTof tofsolver(grid, use_multidim_upwind);

opm/core/transport/reorder/TransportModelTracerTofDiscGal.cpp

@@ -128,8 +128,11 @@ namespace Opm
     /// \param[in] use_cvi   If true, use corner point velocity interpolation.
     ///                      Otherwise, use the basic constant interpolation.
     TransportModelTracerTofDiscGal::TransportModelTracerTofDiscGal(const UnstructuredGrid& grid,
-                                                                   const bool use_cvi)
+                                                                   const bool use_cvi,
+                                                                   const bool use_limiter)
         : grid_(grid),
+          use_cvi_(use_cvi),
+          use_limiter_(use_limiter),
           coord_(grid.dimensions),
           velocity_(grid.dimensions)
     {
@@ -230,17 +233,21 @@ namespace Opm
                 flux = -darcyflux_[face];
                 upstream_cell = grid_.face_cells[2*face];
             }
-            if (upstream_cell < 0) {
-                // This is an outer boundary. Assumed tof = 0 on inflow, so no contribution.
-                continue;
-            }
             if (flux >= 0.0) {
                 // This is an outflow boundary.
                 continue;
             }
+            if (upstream_cell < 0) {
+                // This is an outer boundary. Assumed tof = 0 on inflow, so no contribution.
+                continue;
+            }
             // Do quadrature over the face to compute
             // \int_{\partial K} u_h^{ext} (v(x) \cdot n) b_j ds
             // (where u_h^{ext} is the upstream unknown (tof)).
+            // Quadrature degree set to 2*D, since u_h^{ext} varies
+            // with degree D, and b_j too. We assume that the normal
+            // velocity is constant (this assumption may have to go
+            // for higher order than DG1).
             const double normal_velocity = flux / grid_.face_areas[face];
             FaceQuadrature quad(grid_, face, 2*degree_);
             for (int quad_pt = 0; quad_pt < quad.numQuadPts(); ++quad_pt) {
@@ -358,8 +365,14 @@ namespace Opm
             }
             THROW("Lapack error: " << info << " encountered in cell " << cell);
         }
+
         // The solution ends up in rhs_, so we must copy it.
         std::copy(rhs_.begin(), rhs_.end(), tof_coeff_ + num_basis*cell);
+
+        // Apply limiter.
+        if (degree_ > 0 && use_limiter_) {
+            useLimiter(cell);
+        }
     }
 
 
@@ -376,4 +389,84 @@ namespace Opm
 
 
 
+    void TransportModelTracerTofDiscGal::useLimiter(const int cell)
+    {
+        if (degree_ != 1) {
+            THROW("This limiter only makes sense for our DG1 implementation.");
+        }
+
+        // Limiter principles:
+        // 1. Let M be the minimum TOF value on the upstream faces,
+        //    evaluated in the upstream cells. Then the value at all
+        //    points in this cell shall be at least M.
+        // 2. The TOF shall not be below zero in any point.
+
+        const int dim = grid_.dimensions;
+        const int num_basis = DGBasis::numBasisFunc(dim, degree_);
+
+        double limiter = 1e100;
+        // For inflow faces, ensure that cell tof does not dip below
+        // the minimum value from upstream (for that face).
+        for (int hface = grid_.cell_facepos[cell]; hface < grid_.cell_facepos[cell+1]; ++hface) {
+            const int face = grid_.cell_faces[hface];
+            double flux = 0.0;
+            int upstream_cell = -1;
+            if (cell == grid_.face_cells[2*face]) {
+                flux = darcyflux_[face];
+                upstream_cell = grid_.face_cells[2*face+1];
+            } else {
+                flux = -darcyflux_[face];
+                upstream_cell = grid_.face_cells[2*face];
+            }
+
+            // Evaluate the solution in all corners, and find the appropriate limiter.
+            bool upstream = (upstream_cell >= 0 && flux < 0.0);
+            double min_upstream = upstream ? 1e100 : 0.0;
+            double min_here = 1e100;
+            for (int fnode = grid_.face_nodepos[face]; fnode < grid_.face_nodepos[face+1]; ++fnode) {
+                const double* nc = grid_.node_coordinates + dim*grid_.face_nodes[fnode];
+                DGBasis::eval(grid_, cell, degree_, nc, &basis_[0]);
+                const double tof_here = std::inner_product(basis_.begin(), basis_.end(),
+                                                           tof_coeff_ + num_basis*cell, 0.0);
+                min_here = std::min(min_here, tof_here);
+                if (upstream) {
+                    DGBasis::eval(grid_, upstream_cell, degree_, nc, &basis_nb_[0]);
+                    const double tof_upstream
+                        = std::inner_product(basis_nb_.begin(), basis_nb_.end(),
+                                             tof_coeff_ + num_basis*upstream_cell, 0.0);
+                    min_upstream = std::min(min_upstream, tof_upstream);
+                }
+            }
+            if (min_here < min_upstream) {
+                // Must limit slope.
+                const double tof_c = tof_coeff_[num_basis*cell];
+                if (tof_c < min_upstream) {
+                    // Handle by setting a flat solution.
+                    std::cout << "Trouble in cell " << cell << std::endl;
+                    limiter = 0.0;
+                    tof_coeff_[num_basis*cell] = min_upstream;
+                    break;
+                }
+                const double face_limit = (tof_c - min_upstream)/(tof_c - min_here);
+                limiter = std::min(limiter, face_limit);
+            }
+        }
+
+        if (limiter < 0.0) {
+            THROW("Error in limiter.");
+        }
+
+        if (limiter < 1.0) {
+            std::cout << "Applying limiter in cell " << cell << ", limiter = " << limiter << std::endl;
+            for (int i = num_basis*cell + 1; i < num_basis*(cell+1); ++i) {
+                tof_coeff_[i] *= limiter;
+            }
+        } else {
+            std::cout << "Not applying limiter in cell " << cell << "!" << std::endl;
+        }
+    }
+
+
+
+
 } // namespace Opm

opm/core/transport/reorder/TransportModelTracerTofDiscGal.hpp

@@ -51,7 +51,8 @@ namespace Opm
         /// \param[in] use_cvi   If true, use corner point velocity interpolation.
         ///                      Otherwise, use the basic constant interpolation.
         TransportModelTracerTofDiscGal(const UnstructuredGrid& grid,
-                                       const bool use_cvi);
+                                       const bool use_cvi,
+                                       const bool use_limiter = false);
 
 
         /// Solve for time-of-flight.
@@ -82,9 +83,11 @@ namespace Opm
         TransportModelTracerTofDiscGal(const TransportModelTracerTofDiscGal&);
         TransportModelTracerTofDiscGal& operator=(const TransportModelTracerTofDiscGal&);
 
+        // Data members
         const UnstructuredGrid& grid_;
         boost::shared_ptr<VelocityInterpolationInterface> velocity_interpolation_;
         bool use_cvi_;
+        bool use_limiter_;
         const double* darcyflux_;   // one flux per grid face
         const double* porevolume_;  // one volume per cell
         const double* source_;      // one volumetric source term per cell
@@ -100,6 +103,9 @@ namespace Opm
         std::vector<double> basis_nb_;
         std::vector<double> grad_basis_;
         std::vector<double> velocity_;
+
+        // Private methods
+        void useLimiter(const int cell);
     };
 
 } // namespace Opm