Knudsen Number Effects on Two-Dimensional Rayleigh-Taylor Instability in Compressible Fluid: Based on a Discrete Boltzmann Method

Haiyan Ye; Huilin Lai; Demei Li; Yanbiao Gan; Chuandong Lin; Lu Chen; Aiguo Xu

doi:10.3390/e22050500

Knudsen Number Effects on Two-Dimensional Rayleigh-Taylor Instability in Compressible Fluid: Based on a Discrete Boltzmann Method

Entropy (Basel). 2020 Apr 26;22(5):500. doi: 10.3390/e22050500.

Authors

Haiyan Ye¹, Huilin Lai¹, Demei Li¹, Yanbiao Gan², Chuandong Lin³, Lu Chen¹, Aiguo Xu^{4

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Affiliations

¹ College of Mathematics and Informatics, FJKLMAA, Fujian Normal University, Fuzhou 350117, China.
² North China Institute of Aerospace Engineering, Langfang 065000, China.
³ Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China.
⁴ Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-26, Beijing 100088, China.
⁵ State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China.
⁶ Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, College of Engineering, Peking University, Beijing 100871, China.

Abstract

Based on the framework of our previous work [H.L. Lai et al., Phys. Rev. E, 94, 023106 (2016)], we continue to study the effects of Knudsen number on two-dimensional Rayleigh-Taylor (RT) instability in compressible fluid via the discrete Boltzmann method. It is found that the Knudsen number effects strongly inhibit the RT instability but always enormously strengthen both the global hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE) effects. Moreover, when Knudsen number increases, the Kelvin-Helmholtz instability induced by the development of the RT instability is difficult to sufficiently develop in the later stage. Different from the traditional computational fluid dynamics, the discrete Boltzmann method further presents a wealth of non-equilibrium information. Specifically, the two-dimensional TNE quantities demonstrate that, far from the disturbance interface, the value of TNE strength is basically zero; the TNE effects are mainly concentrated on both sides of the interface, which is closely related to the gradient of macroscopic quantities. The global TNE first decreases then increases with evolution. The relevant physical mechanisms are analyzed and discussed.

Keywords: Knudsen number; Rayleigh–Taylor instability; compressible fluid; discrete Boltzmann method; non-equilibrium effects.