Volume 14, Issue 6
Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium

Adv. Appl. Math. Mech., 14 (2022), pp. 1433-1455.

Published online: 2022-08

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• 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.

65M06, 65M12, 65M15, 65M55

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@Article{AAMM-14-1433, author = {Zhang , Jing and Rui , Hongxing}, title = {Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {6}, pages = {1433--1455}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0187}, url = {http://global-sci.org/intro/article_detail/aamm/20854.html} }
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.

Jing Zhang & Hongxing Rui. (2022). Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium. Advances in Applied Mathematics and Mechanics. 14 (6). 1433-1455. doi:10.4208/aamm.OA-2021-0187
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