Numerical solution of a miscible displacement problem with dispersion term using a two-grid mixed finite element approach

Abstract

A nonlinear system of two coupled partial differential equations is derived to describe miscible displacement of one incompressible fluid by another in a porous medium. A mixed finite element method (MFEM) is applied to the pressure equation, and the mixed finite element method with characteristics(CMFEM) is proposed to solve the concentration equation. A two-grid algorithm is considered to linearize nonlinear system of two coupled partial differential equations models. Moreover, the error estimates are carried out for the two-grid algorithm in this paper. Numerical experiments are presented to show the efficiency of the two-grid algorithm.