Modified Method of Characteristics Combined with Finite Volume Element Methods for Incompressible Miscible Displacement Problems in Porous Media

Abstract EN

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.

In this paper, we present a mixed finite volume element method (FVEM) for the approximation of the pressure-velocity equation.

Since modified method of characteristics (MMOC) minimizes the grid orientation effect, for the approximation of the concentration equation, we apply a standard FVEM combined with MMOC.

A priori error estimates in L∞(L2) norm are derived for velocity, pressure and concentration.

Numerical results are presented to substantiate the validity of the theoretical results.