A numerical method for coupling the BGK model and Euler equations through the linearized Knudsen layer

JOURNAL OF COMPUTATIONAL PHYSICS

卷:398

Article

Chen, Hongxu¹  Li, Qin¹  Lu, Jianfeng^2,3 

[1] Univ Wisconsin Madison, Math Dept, 480 Lincoln Dr, Madison, WI 53705 USA

[2] Duke Univ, Dept Phys, Dept Math, Box 90320, Durham, NC 27708 USA

[3] Duke Univ, Dept Chem, Box 90320, Durham, NC 27708 USA

关键词: BGK model;    Kinetic-fluid coupling;    Domain decomposition;    Euler equations;   

DOI  :  10.1016/j.jcp.2019.108893

来源: Elsevier

【 摘 要 】

The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is small. In practice, however, Knudsen layers emerge at the physical boundary, or at the interfaces between the two regimes. We model the Knudsen layer using a half-space kinetic equation, and apply a half-space numerical solver[ 19,20] to quantify the transition between the kinetic to the fluid regime. A full domain numerical solver is developed with a domain-decomposition approach, where we apply the Euler solver and kinetic solver on the appropriate subdomains and connect them via the half-space solver. In the nonlinear case, linearization is performed upon local Maxwellian. Despite the lack of analytical support, the numerical evidence nevertheless demonstrate that the linearization approach is promising. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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