Discrete ellipsoidal statistical BGK model and Burnett equations  

作　　者：Yu-Dong Zhang Ai-Guo Xu Guang-Cai Zhang Zhi-Hua Chen Pei Wang 

机构地区：[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

出　　处：《Frontiers of physics》2018年第3期149-161,共13页物理学前沿（英文版）

基　　金：The authors would like to acknowledge the support of the National Natural Science Foundation of China （Grant Nos. 11475028, 11772064, 11502117, and U1530261）, and Science Challenge Project （Grant Nos. JCKY2016212A501 and TZ2016002）.

摘　　要：A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook （ES- BGK） 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.A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook （ES- BGK） 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.

关 键 词：discrete Boltzmann model eUipsoidal statistical BGK Burnett equations nonequilibriumquantities actual distribution function 

分 类 号：O122.2[理学—数学] P631.443[理学—基础数学]