Volume 22, Issue 4
A Two-Stage Fourth-Order Gas-Kinetic Scheme for Compressible Multicomponent Flows

Liang Pan, Junxia Cheng, Shuanghu Wang & Kun Xu

Commun. Comput. Phys., 22 (2017), pp. 1123-1149.

Published online: 2017-10

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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.

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@Article{CiCP-22-1123, author = {}, title = {A Two-Stage Fourth-Order Gas-Kinetic Scheme for Compressible Multicomponent Flows}, journal = {Communications in Computational Physics}, year = {2017}, volume = {22}, number = {4}, pages = {1123--1149}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0023}, url = {http://global-sci.org/intro/article_detail/cicp/9996.html} }
TY - JOUR T1 - A Two-Stage Fourth-Order Gas-Kinetic Scheme for Compressible Multicomponent Flows JO - Communications in Computational Physics VL - 4 SP - 1123 EP - 1149 PY - 2017 DA - 2017/10 SN - 22 DO - http://doi.org/10.4208/cicp.OA-2017-0023 UR - https://global-sci.org/intro/article_detail/cicp/9996.html KW - AB -

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.

Liang Pan, Junxia Cheng, Shuanghu Wang & Kun Xu. (2020). A Two-Stage Fourth-Order Gas-Kinetic Scheme for Compressible Multicomponent Flows. Communications in Computational Physics. 22 (4). 1123-1149. doi:10.4208/cicp.OA-2017-0023
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