Sequential Semi-Implicit Algorithm for Computing Discontinuous Flows in Porous Media

by M. A. Vegas-Landeau, R. Propp, P. Colella, Tadeusz W. Patzek
Year: 1998


Vegas-Landeau, M. A., Rick Propp, T. W. Patzek, and Phillip Colella. "Sequential semi-implicit algorithm for computing discontinuous flows in porous media." SPE Journal 3, no. 02 (1998): 200-208.


A novel numerical algorithm for computing incompressible, discontinuous, two-phase flows in two-dimensional, inhomogeneous, and isotropic porous media is presented. The algorithm uses Colella et al`s. hybrid sequential explicit-implicit approach for both accuracy and speed of the calculations. The explicit part uses a high-order Godunov scheme with a modified Van Leer geometrical slope limiter, similar to those used in shock dynamics. The implicit part is a two-step solver: the first step is a Crank-Nicolson saturation solver and the second one is a Poisson solver for the phase pressure. Both use fast multilevel multigrid solvers with the number of operations of the order of {var_theta}[Nlog(N)], where N is the number of grid points. For an implicit simulator, the number of operations is {var_theta}(N{sup 3}) per time step. Two numerically stiff reservoir engineering problems are presented to demonstrate the low numerical dispersion and second-order accuracy of our method.