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 - <p style="text-align: justify;">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.</p>