Computational multiscale methods for quasi-gas dynamic equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:440

Article

Chetverushkin, Boris¹  Chung, Eric²  Efendiev, Yalchin^3,4,5  Pun, Sai-Mang³  Zhang, Zecheng³ 

[1] Russian Acad Sci, Keldysh Inst Appl Math, Moscow, Russia

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

[3] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[4] Texas A&M Univ, Inst Sci Comp, College Stn, TX 77843 USA

[5] North Eastern Fed Univ, Multiscale Model Reduct, Yakutsk 677007, Republic Of Sak, Russia

关键词: Multiscale;    Constraint energy minimizing;    Generalized multiscale finite element;    Quasi gas dynamics;   

DOI  :  10.1016/j.jcp.2021.110352

来源: Elsevier

【 摘 要 】

In this paper, we consider the quasi-gas-dynamic (QGD) model in a multiscale environment. The model equations can be regarded as a hyperbolic regularization and are derived from kinetic equations. So far, the research on QGD models has been focused on problems with constant coefficients. In this paper, we investigate the QGD model in multiscale media, which can be used in porous media applications. This multiscale problem is interesting from a multiscale methodology point of view as the model problem has a hyperbolic multiscale term, and designing multiscale methods for hyperbolic equations is challenging. In the paper, we apply the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) combined with the central difference scheme in time to solve this problem. The CEM-GMsFEM provides a flexible and systematical framework to construct crucial multiscale basis functions for approximating the solution to the problem with reduced computational cost. With this approach of spatial discretization, we establish the stability of the fully discretized scheme, based on the coarse grid, under a coarse-scale CFL condition. Complete convergence analysis of the proposed method is presented. Numerical results are provided to illustrate and verify the theoretical findings. (C) 2021 Published by Elsevier Inc.

【 授权许可】

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