TY - JOUR T1 - Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium AU - Zhang , Jing AU - Rui , Hongxing JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1433 EP - 1455 PY - 2022 DA - 2022/08 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2021-0187 UR - https://global-sci.org/intro/article_detail/aamm/20854.html KW - Porous media, two phase flow, block-centered finite difference, two-grid, numerical analysis. AB -

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.