Finite Volume Approximations for Incompressible Miscible Displacement Problems in Porous Media with Modified Method of Characteristics

Abstract

The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure-velocity equation and the concentration equation. The pressure-velocity is elliptic type and the concentration equations is convection dominated diffusion type. It is known that miscible displacement problems follow the natural law of conservation and finite volume methods are conservative. Hence, in this paper, we present a mixed finite volume element method FVEM for the approximation of the pressure-velocity equation. Since concentration equation is convection dominated diffusion type and most of the numerical methods suffer from the grid orientation effect and modified method of characteristicsMMOC minimizes the grid orientation effect. Therefore, for the approximation of the concentration equation we apply a standard FVEM combined MMOC. A priori error estimates are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.