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题名	PATH-CONSERVATIVE CENTRAL-UPWIND SCHEMES FOR NONCONSERVATIVE HYPERBOLIC SYSTEMS
作者	Castro Diaz, Manuel Jesus 1; Kurganov, Alexander2,3 ; Morales de Luna, Tomas 4
通讯作者	Kurganov, Alexander
发表日期	2019-06-21
DOI	10.1051/m2an/2018077
发表期刊	ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 影响因子和分区
ISSN	0764-583X
EISSN	1290-3841
卷号	53 期号:3页码:959-985
摘要	We develop path-conservative central-upwind schemes for nonconservative one-dimensional hyperbolic systems of nonlinear partial differential equations. Such systems arise in a variety of applications and the most challenging part of their numerical discretization is a robust treatment of nonconservative product terms. Godunov-type central-upwind schemes were developed as an efficient, highly accurate and robust "black-box" solver for hyperbolic systems of conservation and balance laws. They were successfully applied to a large number of hyperbolic systems including several nonconservative ones. To overcome the difficulties related to the presence of nonconservative product terms, several special techniques were proposed. However, none of these techniques was sufficiently robust and thus the applicability of the original central-upwind schemes was rather limited. In this paper, we rewrite the central-upwind schemes in the form of path-conservative schemes. This helps us (i) to show that the main drawback of the original central-upwind approach was the fact that the jump of the nonconservative product terms across cell interfaces has never been taken into account and (ii) to understand how the nonconservative products should be discretized so that their influence on the numerical solution is accurately taken into account. The resulting path-conservative central-upwind scheme is a new robust tool for both conservative and nonconservative hyperbolic systems. We apply the new scheme to the Saint-Venant system with discontinuous bottom topography and two-layer shallow water system. Our numerical results illustrate the good performance of the new path-conservative central-upwind scheme, its robustness and ability to achieve very high resolution.
关键词	Nonconservative hyperbolic systems of PDEs Saint-Venant system two-layer shallow water equations central-upwind scheme path-conservative scheme well-balanced scheme
相关链接	[来源记录]
收录类别	SCI ; EI
语种	英语
学校署名	通讯
资助项目	NSF[DMS-1521009] ; NSF[DMS-1818666]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000475769100002
出版者	EDP SCIENCES S A
EI入藏号	20192807155282
EI主题词	Equations of motion ; Partial differential equations ; Topography
EI分类号	Calculus:921.2 ; Materials Science:951
ESI学科分类	MATHEMATICS
来源库	Web of Science
引用统计	被引频次[WOS]：25
成果类型	期刊论文
条目标识符	//www.snoollab.com/handle/2SGJ60CL/25666
专题	理学院_数学系工学院_材料科学与工程系
作者单位	1.Univ Malaga, Dept Anal Matemat, Malaga 29080, Spain 2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China 3.Tulane Univ, Math Dept, New Orleans, LA 70118 USA 4.Univ Cordoba, Dept Matemat, Campus Rabanales, E-14071 Cordoba, Spain
通讯作者单位	数学系
推荐引用方式 GB/T 7714	Castro Diaz, Manuel Jesus,Kurganov, Alexander,Morales de Luna, Tomas. PATH-CONSERVATIVE CENTRAL-UPWIND SCHEMES FOR NONCONSERVATIVE HYPERBOLIC SYSTEMS[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,2019,53(3):959-985.
APA	Castro Diaz, Manuel Jesus,Kurganov, Alexander,&Morales de Luna, Tomas.(2019).PATH-CONSERVATIVE CENTRAL-UPWIND SCHEMES FOR NONCONSERVATIVE HYPERBOLIC SYSTEMS.ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,53(3),959-985.
MLA	Castro Diaz, Manuel Jesus,et al."PATH-CONSERVATIVE CENTRAL-UPWIND SCHEMES FOR NONCONSERVATIVE HYPERBOLIC SYSTEMS".ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 53.3(2019):959-985.