Discrete ellipsoidal statistical BGK model and Burnett equations

doi:10.1007/s11467-018-0749-3

Front. Phys.

2018, Vol. 13

Issue (3) : 135101 https://doi.org/10.1007/s11467-018-0749-3

RESEARCH ARTICLE

Discrete ellipsoidal statistical BGK model and Burnett equations

Yu-Dong Zhang^1,², Ai-Guo Xu^2,³(

), Guang-Cai Zhang², Zhi-Hua Chen¹, Pei Wang²

¹. Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing 210094, China
². Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
³. Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, College of Engineering, Peking University, Beijing 100871, China

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Abstract

A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar–Gross–Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier–Stokes or the Burnett equations.

Keywords discrete Boltzmann model ellipsoidal statistical BGK Burnett equations nonequilibrium quantities actual distribution function

Corresponding Author(s): Ai-Guo Xu

Issue Date: 07 March 2018

Cite this article:

Yu-Dong Zhang,Ai-Guo Xu,Guang-Cai Zhang, et al. Discrete ellipsoidal statistical BGK model and Burnett equations[J]. Front. Phys. , 2018, 13(3): 135101.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-018-0749-3
https://academic.hep.com.cn/fop/EN/Y2018/V13/I3/135101

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