Discretisation and Multigrid Solution of Elliptic Equations with Mixed Derivative Terms and Strongly Discontinuous Coefficients

M-Matrix Flux Splitting for General Full Tensor Discretization Operators on Structured and Unstructured Grids

“…Full tensor approximation is a particularly important issue for flow in porous media [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. A major assumption in most commercial simulators is that the flux depends on a diagonal tensor and that the consequent discretizations employ minimal five-and sevennode operators.…”

A Rotated Monotone Difference Scheme for the Two-Dimensional Anisotropic Drift-Diffusion Equation

“…Hence the discrete system will never be an M-matrix irrespective of the grid size h and k. This hurdle is purely due to the way the mixed derivative term is discretized. This is precisely the reason Tapiero and Sulem [6], Asencor and Panizo [11], and Crumpton et al [4] could not attain discrete maximum principles in their discretization. It may be noted here that the above conclusion is independent of the way the Neumann boundary condition (6) is discretized.…”

“…Similarly, in the presence of mechanical stress, carrier transport in the semiconductor device becomes anisotropic by virtue of piezoresistance [3]. The anisotropic diffusion equation also governs flow in porous media, pertinent to reservoir simulation problems, as well as the transport of atmospheric gases [4,5]. The PDE (1) is called the Hamilton-Jacobi-Bellman equation which governs the dynamics of any stochastic optimal control problem when the underlying processes are driven by Brownian motion [6].…”

Stabilized velocity post‐processings for Darcy flow in heterogeneous porous media

“…This test problem from Crumpton et al [21] is defined on the square where the parameter is used to vary the strength of the discontinuity at x = 0. In our experiments we used = 1.0.…”