An Upwind Mixed Finite Element Method on Changing Meshes for Positive Semi-Definite Oil-Water Displacement of Darcy-Forchheimer Flow in Porous Media

Abstract

An upwind mixed finite element method is proposed on changing meshes for solving a positive semi-definite miscible displacement problem of Darcy-Forchheimer flow in three-dimensional porous media. The pressure and velocity could be obtained together by using a mixed finite element, and the computational accuracy of velocity is improved. The concentration equation is solved by the upwind mixed finite element scheme on changing meshes, where the upwind approximation and an expanded mixed finite element are adopted for the convection and diffusion, respectively. It solves the convection-dominated diffusion problem well and has the following improvements. First, the conservation of mass, an important physical nature, is preserved. Second, it has high order computational accuracy. An optimal-order error estimates is concluded. Numerical experiments illustrate the efficiency and application of the presented scheme.