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A Two-Stage Fourth-Order Gas-Kinetic Scheme for Compressible Multicomponent Flows

Part of: Compressible fluids and gas dynamics, general Two-phase and multiphase flows Rarefied gas flows, Boltzmann equation

Published online by Cambridge University Press:  28 July 2017

Liang Pan ,
Junxia Cheng ,
Shuanghu Wang  and
Kun Xu
Liang Pan*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing, China
Junxia Cheng*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing, China
Shuanghu Wang*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing, China
Kun Xu*
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
*
*Corresponding author. Email addresses:panliangjlu@sina.com (L. Pan), cheng_junxia@iapcm.ac.cn (J. X. Cheng), wang_shuanghu@iapcm.ac.cn (S. H. Wang), makxu@ust.hk (K. Xu)
*Corresponding author. Email addresses:panliangjlu@sina.com (L. Pan), cheng_junxia@iapcm.ac.cn (J. X. Cheng), wang_shuanghu@iapcm.ac.cn (S. H. Wang), makxu@ust.hk (K. Xu)
*Corresponding author. Email addresses:panliangjlu@sina.com (L. Pan), cheng_junxia@iapcm.ac.cn (J. X. Cheng), wang_shuanghu@iapcm.ac.cn (S. H. Wang), makxu@ust.hk (K. Xu)
*Corresponding author. Email addresses:panliangjlu@sina.com (L. Pan), cheng_junxia@iapcm.ac.cn (J. X. Cheng), wang_shuanghu@iapcm.ac.cn (S. H. Wang), makxu@ust.hk (K. Xu)
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Abstract

With the use of temporal derivative of flux function, a two-stage temporal discretization has been recently proposed in the design of fourth-order schemes based on the generalized Riemann problem (GRP) [21] and gas-kinetic scheme (GKS) [28]. In this paper, the fourth-order gas-kinetic scheme will be extended to solve the compressible multicomponent flow equations, where the two-stage temporal discretization and fifth-order WENO reconstruction will be used in the construction of the scheme. Based on the simplified two-species BGK model [41], the coupled Euler equations for individual species will be solved. Each component has its individual gas distribution function and the equilibrium states for each component are coupled by the physical requirements of total momentum and energy conservation in particle collisions. The second-order flux function is used to achieve the fourth-order temporal accuracy, and the robustness is as good as the second-order schemes. At the same time, the source terms, such as the gravitational force and the chemical reaction, will be explicitly included in the two-stage temporal discretization through their temporal derivatives. Many numerical tests from the shock-bubble interaction to ZND detonative waves are presented to validate the current approach.

Keywords

Multicomponent flowsgas kinetic schemetwo-stage temporal discretization

MSC classification

Secondary: 76T10: Liquid-gas two-phase flows, bubbly flows 76P05: Rarefied gas flows, Boltzmann equation 76N15: Gas dynamics, general
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 4 , October 2017 , pp. 1123 - 1149
Copyright
Copyright © Global-Science Press 2017 

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