Approximation of the multi-dimensional incompressible Navier-Stokes equations by discrete-velocity vector-BGK models

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Zhao, Jin¹  Zhang, Zhimin¹  Yong, Wen-An² 

[1] Beijing Computat Sci Res Ctr, Div Appl & Computat Math, Beijing 100084, Peoples R China

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

关键词: Vector-BGK model;    Incompressible Navier-Stokes equations;    Maxwell iteration;    Energy estimates;    Convergence-stability lemma;   

DOI  :  10.1016/j.jmaa.2020.123901

来源: Elsevier

【 摘 要 】

In this paper, we prove that a class of discrete-velocity vector-BGK models can be used as approximations to the multi-dimensional incompressible Navier-Stokes equations on the torus. The proof relies crucially on two constructions: a new symmetrizer and approximate solutions. The former renders us a natural setting for energy estimates and the latter is motivated by the Maxwell iteration. Simple and concise stability conditions are also obtained for a number of concrete 2- or 3-dimensional BGK models. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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