A Mixed Volume Element Modified With Characteristic Fractional Step Difference Method for the Compressible Multicomponent Displacement and Its Numerical Analysis

A three-dimensional compressible problem with different components is fundamental in numerical simulation of enhanced oil recovery. The mathematical model consists of a parabolic equation for the pressure and a convection-diffusion system for the concentrations. The pressure determines Darcy velocity and plays an important role during the whole physical process. A conservative mixed volume element is used to discretize the flow equation, and improves the computational accuracy of Darcy. The concentrations are computed by the modified characteristic fractional step difference scheme, thus numerical dispersion and nonphysical oscillations are eliminated. The whole three-dimensional computation is accomplished effectively by solving three successive one-dimensional problems in parallel, where the speedup method is used and the work is decreased greatly. Based on the theory and special techniques of a priori estimates of partial differential equations, an optimal second error estimates in L^2-norm is concluded. This work concentrates on the model, numerical method and convergence analysis for modern oil recovery.