THE TWO-DIMENSIONAL RIEMANN PROBLEM FOR ISENTROPIC CHAPLYGIN GAS DYNAMIC SYSTEM

doi:10.3934/cpaa.2010.9.431

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	THE TWO-DIMENSIONAL RIEMANN PROBLEM FOR ISENTROPIC CHAPLYGIN GAS DYNAMIC SYSTEM
	Guo, Lihui 1,2; Sheng, Wancheng 1; Zhang, Tong 3
	2010-03-01
发表期刊	COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
ISSN	1534-0392
卷号	9 期号:2 页码:431-458
摘要	The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system consists of interactions of four planar elementary waves. Different from polytropic gas, all of them are contact discontinuities due to the system is full linear degenerate, i.e., the three eigenvalues of the system are linear degenerate. They include compressive one (S-+/-), rarefactive one (R-+/-) and slip lines (J(+/-)). We still call S-+/- as shock and R-+/- as rarefaction wave. In this paper, we study the problem systematically. According to different combination of four elementary waves, we deliver a complete classification to the problem. It contains 14 cases in all. The Riemann solutions are self-similar, and the flow is transonic in self-similar plane (x/t, y/t). The boundaries of the interaction domains are obtained. Solutions in supersonic domains are constructed in no J cases. While in the rest cases, the structure of solutions are conjectured except for the case 2J(+) + 2J(-). Especially, delta waves and simple waves appear in some cases. The Dirichlet boundary value problems in subsonic domains or the boundary value problems for transonic flow are formed case by case. The domains are convex for two cases, and non-convex for the rest cases. The boundaries of the domains are composed of sonic curves and/or slip lines.
关键词	2-D Riemann problem Chaplygin gas full linear degenerate delta wave
DOI	10.3934/cpaa.2010.9.431
语种	英语
资助项目	NSFC[10971130] ; Shanghai Leading Academic Discipline Project[J50101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000273229900010
出版者	AMER INST MATHEMATICAL SCIENCES
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10323
专题	中国科学院数学与系统科学研究院
通讯作者	Guo, Lihui
作者单位	1.Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China 2.Coll Math & Syst Sci, Urumqi 830000, Xinjiang, Peoples R China 3.Chinese Acad Sci, Inst Math, AMSS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Guo, Lihui,Sheng, Wancheng,Zhang, Tong. THE TWO-DIMENSIONAL RIEMANN PROBLEM FOR ISENTROPIC CHAPLYGIN GAS DYNAMIC SYSTEM[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2010,9(2):431-458.
APA	Guo, Lihui,Sheng, Wancheng,&Zhang, Tong.(2010).THE TWO-DIMENSIONAL RIEMANN PROBLEM FOR ISENTROPIC CHAPLYGIN GAS DYNAMIC SYSTEM.COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,9(2),431-458.
MLA	Guo, Lihui,et al."THE TWO-DIMENSIONAL RIEMANN PROBLEM FOR ISENTROPIC CHAPLYGIN GAS DYNAMIC SYSTEM".COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 9.2(2010):431-458.