Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium
Year: 2022
Author: Jing Zhang, Hongxing Rui
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 6 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0187
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 6 : pp. 1433–1455
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Porous media two phase flow block-centered finite difference two-grid numerical analysis.
Author Details
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