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题名	Experimental convergence rate study for three shock-capturing schemes and development of highly accurate combined schemes
作者	Chu, Shaoshuai 1 ; Kovyrkina, Olyana A.2; Kurganov, Alexander3,4,5,6 ; Ostapenko, Vladimir V.2
通讯作者	Kurganov, Alexander
发表日期	2023-06-01
DOI	10.1002/num.23053
发表期刊	NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 影响因子和分区
ISSN	0749-159X
EISSN	1098-2426
卷号	39 期号:6页码:4317-4346
摘要	We study experimental convergence rates of three shock-capturing schemes for hyperbolic systems of conservation laws: the second-order central-upwind (CU) scheme, the third-order Rusanov-Burstein-Mirin (RBM), and the fifth-order alternative weighted essentially non-oscillatory (A-WENO) scheme. We use three imbedded grids to define the experimental pointwise, integral, and W-1,1$$ {W}<^>{-1,1} $$ convergence rates. We apply the studied schemes to the shallow water equations and conduct their comprehensive numerical convergence study. We verify that while the studied schemes achieve their formal orders of accuracy on smooth solutions, after the shock formation, a part of the computed solutions is affected by shock propagation and both the pointwise and integral convergence rates reduce there. Moreover, while the W-1,1$$ {W}<^>{-1,1} $$ convergence rates for the CU and A-WENO schemes, which rely on nonlinear stabilization mechanisms, reduce to the first order, the RBM scheme, which utilizes a linear stabilization, is clearly second-order accurate. Finally, relying on the conducted experimental convergence rate study, we develop two new combined schemes based on the RBM and either the CU or A-WENO scheme. The obtained combined schemes can achieve the same high order of accuracy as the RBM scheme in the smooth areas while being non-oscillatory near the shocks.
关键词	combined schemes finite-difference schemes finite-volume methods integral convergence order reduction behind the shocks pointwise convergence
相关链接	[来源记录]
收录类别	SCI ; EI
语种	英语
学校署名	第一 ; 通讯
资助项目	Guangdong Provincial Key Laboratory Of Computational Science And Material Design[2019B030301001] ; National Natural Science Foundation of China["12171226","12111530004"] ; Russian Foundation for Basic Research[21-51-53012] ; Russian Science Foundation[22-11-00060]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:001007616500001
出版者	WILEY
EI入藏号	20232514257804
EI主题词	Equations of motion ; Finite difference method ; Stabilization
EI分类号	Calculus:921.2 ; Numerical Methods:921.6
ESI学科分类	ENGINEERING
来源库	Web of Science
引用统计	被引频次[WOS]：1
成果类型	期刊论文
条目标识符	http://kc.sustech.edu.cn/handle/2SGJ60CL/549061
专题	理学院_数学系
作者单位	1.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China 2.Novosibirsk State Univ, RAS, Lavrentyev Inst Hydrodynam SB, Novosibirsk, Russia 3.Southern Univ Sci & Technol, Shenzhen Int Ctr Math, Dept Math, Shenzhen, Peoples R China 4.Southern Univ Sci & Technol, Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen, Peoples R China 5.Southern Univ Sci & Technol, Shenzhen Int Ctr Math, Dept Math, Shenzhen 518055, Peoples R China 6.Southern Univ Sci & Technol, Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen 518055, Peoples R China
第一作者单位	数学系
通讯作者单位	数学系; 南方科技大学
第一作者的第一单位	数学系
推荐引用方式 GB/T 7714	Chu, Shaoshuai,Kovyrkina, Olyana A.,Kurganov, Alexander,et al. Experimental convergence rate study for three shock-capturing schemes and development of highly accurate combined schemes[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2023,39(6):4317-4346.
APA	Chu, Shaoshuai,Kovyrkina, Olyana A.,Kurganov, Alexander,&Ostapenko, Vladimir V..(2023).Experimental convergence rate study for three shock-capturing schemes and development of highly accurate combined schemes.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,39(6),4317-4346.
MLA	Chu, Shaoshuai,et al."Experimental convergence rate study for three shock-capturing schemes and development of highly accurate combined schemes".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 39.6(2023):4317-4346.