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Discrete Boltzmann model for implosion- and explosionrelated compressible flow with spherical symmetry

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Abstract

To kinetically model implosion- and explosion-related phenomena, we present a theoretical framework for constructing a discrete Boltzmann model (DBM) with spherical symmetry in spherical coordinates. To achieve this goal, a key technique is to use local Cartesian coordinates to describe the particle velocity in the kinetic model. Therefore, geometric effects, such as divergence and convergence, are described as a “force term”. To better access the nonequilibrium behavior, even though the corresponding hydrodynamic model is one-dimensional, the DBM uses a discrete velocity model (DVM) with three dimensions. A new scheme is introduced so that the DBM can use the same DVM regardless of whether or not there are extra degrees of freedom. As an example, a DVM with 26 velocities is formulated to construct the DBM at the Navier–Stokes level. Via the DBM, one can study simultaneously the hydrodynamic and thermodynamic nonequilibrium behaviors in implosion and explosion processes that are not very close to the spherical center. The extension of the current model to a multiple-relaxation-time version is straightforward.

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Acknowledgements

The authors would like to thank Drs. Chuandong Lin, Yanbiao Gan, and Feng Chen for helpful discussions. The work was supported by the National Natural Science Foundation of China [under Grant Nos. 11475028, 11772064, and U1530261] and the Science Challenge Project (under Grant Nos. JCKY2016212A501 and TZ2016002).

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Authors and Affiliations

  1. National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-26, Beijing, 100088, China

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

  2. 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

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

    Yu-Dong Zhang

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  1. Ai-Guo Xu
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  2. Guang-Cai Zhang
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Correspondence to Ai-Guo Xu.

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Xu, AG., Zhang, GC., Zhang, YD. et al. Discrete Boltzmann model for implosion- and explosionrelated compressible flow with spherical symmetry. Front. Phys. 13, 135102 (2018). https://doi.org/10.1007/s11467-018-0777-z

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