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Discrete ellipsoidal statistical BGK model and Burnett equations

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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.

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Acknowledgements

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).

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Authors and Affiliations

  1. Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing, 210094, China

    Yu-Dong Zhang & Zhi-Hua Chen

  2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Yu-Dong Zhang, Ai-Guo Xu, Guang-Cai Zhang & Pei Wang

  3. Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, College of Engineering, Peking University, Beijing, 100871, China

    Ai-Guo Xu

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  1. Yu-Dong Zhang
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Correspondence to Ai-Guo Xu.

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Zhang, YD., Xu, AG., Zhang, GC. et al. Discrete ellipsoidal statistical BGK model and Burnett equations. Front. Phys. 13, 135101 (2018). https://doi.org/10.1007/s11467-018-0749-3

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  • DOI: https://doi.org/10.1007/s11467-018-0749-3

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