Simulation of miscible displacement in porous media by a modified Uzawaʹs algorithm combined with a characteristic method Original Research Article

Miscible displacement in porous media is modeled by a nonlinear coupled system of two partial differential equations: the pressure equation, which is elliptic, and the concentration equation, which is parabolic but usually convection-dominated. In this paper, we focus on some computational difficulties in the simulation of this problem. In order to obtain accurate approximation for velocity, we implement a modified Uzawaʹs algorithm for the pressure equation with a full permeability tensor including strong heterogeneity and anisotropy. For handling the convection dominance over diffusion, we employ a modified method of characteristics for the concentration equation. Numerical simulation results show that the combination of the modified method of characteristics and the modified Uzawaʹs algorithm is a good choice for the problem. In particular, the modified method of characteristics dramatically reduces numerical diffusion and non-physical oscillation in the approximate concentration, and the modified Uzawaʹs algorithm leads to positive definite linear systems with velocity unknowns only and exhibits the accuracy of mixed finite element methods.