Highly efficient numerical algorithm for compressible miscible displacement problem involving dispersion term

Purpose The purpose of this paper is to present an efficient improved version of a characteristic mixed finite element (CMFE) method for the compressible miscible displacement problem with a dispersion term in a porous medium. Design/methodology/approach The compressible miscible displacement problem with a dispersion term in a porous medium resulted in the derivation of a nonlinear parabolic system, which is more nonlinear and coupling. The authors apply mixed finite element method to approximate the pressure equation and a CMFE method to discrete the concentration equation. Then, two-grid method is used to speed up computation without losing accuracy, thus to increase the efficiency of the method. Findings Using a CMFE two-grid method can reduce CPU time and without losing accuracy. Because equation (1.1) shows often hyperbolic, a CMFE method is more effective to solve such a coupled system. Originality/value This paper describes a CMFE two-grid method that solves the compressible miscible displacement problem with a dispersion term in a porous medium. This method is an efficient algorithm as it maintains accuracy and saves computation time. Under certain assumptions, error estimates for the two-grid solution are obtained by using Lq error estimates of CMFE methods.