Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium (Advances in Applied Mathematics and Mechanics, 2022)
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 linearequation on fine grid of size $h.$ We establish the full discrete two-grid block-centeredfinite difference scheme on a uniform grid. The error estimates for the pressure, Darcyvelocity, concentration variables are derived, which show that the discrete $L_2$ erroris $\mathcal{O}(∆t+h^2+H^4).$ Finally, two numerical examples are provided to demonstrate theeffectiveness and accuracy of our algorithm.