General synthetic iterative scheme for nonlinear gas kinetic simulation of multi-scale rarefied gas flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:430

Article

Zhu, Lianhua¹  Pi, Xingcai²  Su, Wei³  Li, Zhi-Hui^2,4  Zhang, Yonghao³  Wu, Lei⁵ 

[1] Univ Strathclyde, Dept Mech & Aerosp Engn, James Weir Fluids Lab, Glasgow G1 1XJ, Lanark, Scotland

[2] China Aerodynam Res & Dev Ctr, Hyperveloc Aerodynam Inst, Mianyang 621000, Peoples R China

[3] Univ Edinburgh, Sch Engn, Edinburgh EH9 3FB, Midlothian, Scotland

[4] Natl Lab Computat Fluid Dynam, Beijing 100191, Peoples R China

[5] Southern Univ Sci & Technol, Dept Mech & Aerosp Engn, Shenzhen 518055, Peoples R China

关键词: Gas kinetic equation;    Multi-scale rarefied gas flows;    Fourier stability analysis;    General synthetic iterative scheme;    Fast convergence;   

DOI  :  10.1016/j.jcp.2020.110091

来源: Elsevier

【 摘 要 】

The general synthetic iterative scheme (GSIS) is extended to find the steady-state solution of the nonlinear gas kinetic equation, resolving the long-standing problems of slow convergence and requirement of ultra-fine grids in near-continuum flows. The key ingredient of GSIS is the tight coupling of gas kinetic and macroscopic synthetic equations, where the constitutive relations explicitly contain Newton's law of shear stress and Fourier's law of heat conduction. The higher-order constitutive relations describing rarefaction effects are calculated from the velocity distribution function; however, their constructions are simpler than our previous work (Su et al., 2020 [28]) for linearized gas kinetic equations. On the other hand, solutions of macroscopic synthetic equations are used to accelerate the evolution of gas kinetic equation at the next iteration step. A rigorous linear Fourier stability analysis of the present schemes in periodic system shows that the error decay rate of GSIS can be smaller than 0.5, which means that the deviation to steady-state solution can be reduced by 3 orders of magnitude in 10 iterations. Other important advantages of the GSIS are: (i) it does not rely on the specific form of Boltzmann collision operator, and (ii) it can be solved by sophisticated techniques in computational fluid dynamics, making it amenable to large scale engineering applications. In this paper, the efficiency and accuracy of GSIS are demonstrated by a number of canonical test cases in rarefied gas dynamics, covering different flow regimes. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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