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

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 L2 error is O(Dt+h2+H4).Finally,two numerical examples are provided to demonstrate the effectiveness and accuracy of our algorithm.