Commun. Comput. Phys., 14 (2013), pp. 1347-1371.


A Gas Kinetic Scheme for the Simulation of Compressible Multicomponent Flows

Liang Pan 1, Guiping Zhao 2, Baolin Tian 3, Shuanghu Wang 3*

1 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China; The Graduate School of China Academy of Engineering Physics, Beijing 100088, China.
2 National Natural Science Foundation of China, Beijing 100085, China.
3 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China.

Received 28 March 2012; Accepted (in revised version) 21 March 2013
Available online 5 July 2013
doi:10.4208/cicp.280312.210313a

Abstract

In this paper, a gas kinetic scheme for the compressible multicomponent flows is presented by making use of two-species BGK model in [A. D. Kotelnikov and D. C. Montgomery, A Kinetic Method for Computing Inhomogeneous Fluid Behavior, J. Comput. Phys. 134 (1997) 364-388]. Different from the conventional BGK model, the collisions between different species are taken into consideration. Based on the Chapman-Enskog expansion, the corresponding macroscopic equations are derived from this two-species model. Because of the relaxation terms in the governing equations, the method of operator splitting is applied. In the hyperbolic part, the integral solutions of the BGK equations are used to construct the numerical fluxes at the cell interface in the framework of finite volume method. Numerical tests are presented in this paper to validate the current approach for the compressible multicomponent flows. The theoretical analysis on the spurious oscillations at the interface is also presented.

AMS subject classifications: 76T10, 76P05, 76N15

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Key words: Multicomponent flows, two-species BGK model, Chapman-Enskog expansion, gas kinetic scheme.

*Corresponding author.
Email: panliangjlu@sina.com (L. Pan), zhaogp@nsfc.gov.cn (G. Zhao), tian_baolin@iapcm.ac.cn (B. Tian), wang_shuanghu@iapcm.ac.cn (S. Wang)
 

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