Characteristics difference method for incompressible miscible flow in porous media

Two-phase, incompressible miscible flow in prous media is governed by a system of nonlinear partial differential equations. The pressure equation, which is elliptic in appearance, is discretized by a standard five-points difference method. The concentration equation is treated by an implicit finite difference method that applies a form of the method of characteristics to the transport terms. A class of biquadratic interpolation is introduced for the method of characteristics. Convergene rate is proved to be O(Δt+h ²). This work is supported by National Natural Science Foundation of China and the Doctoral Foundation of National Education Ministry.