Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium

Abstract

In this paper, a two-grid block-centered finite difference method for the incompressible miscible displacement in porous medium is introduced and analyzed, which is to solve a nonlinear equation on coarse mesh space of size $H$ and a linear equation on fine grid of size $h.$ We establish the full discrete two-grid block-centered finite difference scheme on a uniform grid. The error estimates for the pressure, Darcy velocity, concentration variables are derived, which show that the discrete $L_2$ error is $\mathcal{O}(∆t+h^2+H^4 ).$ Finally, two numerical examples are provided to demonstrate the effectiveness and accuracy of our algorithm.