A WELL-BALANCED SYMPLECTICITY-PRESERVING GAS-KINETIC SCHEME FOR HYDRODYNAMIC EQUATIONS UNDER GRAVITATIONAL FIELD

doi:10.1137/100803699

CSpace

	A WELL-BALANCED SYMPLECTICITY-PRESERVING GAS-KINETIC SCHEME FOR HYDRODYNAMIC EQUATIONS UNDER GRAVITATIONAL FIELD
	Luo, Jun 1; Xu, Kun 1; Liu, Na 2
	2011
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	33 期号:5 页码:2356-2381
摘要	A well-balanced scheme for an isolated gravitational hydrodynamic system is defined as a scheme which exactly preserves an isothermal hydrostatic solution. In this paper, a well-balanced gas-kinetic symplecticity-preserving BGK (SP-BGK) scheme is developed. In the construction of the scheme, the gravitational potential is modeled as a piecewise constant function inside each cell with a potential jump at the cell interface. In the process of designing such a scheme, the energy conservation, Liouville's theorem, and the symplecticity-preserving property of a Hamiltonian flow play important roles in the description of particles penetration and reflection from a potential barrier. More importantly, the use of the symplecticity-preserving property is crucial in the evaluation of the moments of a postinteraction gas distribution function with a potential jump in terms of the moments of preinteraction distribution function. The SP-BGK method is the first well-balanced shock-capturing gas-kinetic scheme for the Navier-Stokes equation. A few theorems are proved for this scheme, which include the necessity to use an exact Maxwellian for keeping the isothermal hydrostatic state, the total mass and energy (the sum of kinetic, thermal, and gravitational ones) conservation, and the well-balanced property of the SP-BGK scheme to keep an isothermal hydrostatic state during the process of particle transport and collision. Many numerical examples are presented to validate the SP-BGK scheme.
关键词	gas-kinetic scheme hydrodynamic equations gravitational potential symplecticity preserving well-balanced scheme
DOI	10.1137/100803699
语种	英语
资助项目	Hong Kong Research Grant Council[621709] ; Hong Kong Research Grant Council[RPC10SC11] ; National Natural Science Foundation of China[10928205] ; National Key Basic Research Program[2009CB724101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000296591200011
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13087
专题	中国科学院数学与系统科学研究院
通讯作者	Luo, Jun
作者单位	1.Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Luo, Jun,Xu, Kun,Liu, Na. A WELL-BALANCED SYMPLECTICITY-PRESERVING GAS-KINETIC SCHEME FOR HYDRODYNAMIC EQUATIONS UNDER GRAVITATIONAL FIELD[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2011,33(5):2356-2381.
APA	Luo, Jun,Xu, Kun,&Liu, Na.(2011).A WELL-BALANCED SYMPLECTICITY-PRESERVING GAS-KINETIC SCHEME FOR HYDRODYNAMIC EQUATIONS UNDER GRAVITATIONAL FIELD.SIAM JOURNAL ON SCIENTIFIC COMPUTING,33(5),2356-2381.
MLA	Luo, Jun,et al."A WELL-BALANCED SYMPLECTICITY-PRESERVING GAS-KINETIC SCHEME FOR HYDRODYNAMIC EQUATIONS UNDER GRAVITATIONAL FIELD".SIAM JOURNAL ON SCIENTIFIC COMPUTING 33.5(2011):2356-2381.