Modified Stencil Approximations for Fifth-Order Weighted Essentially Non-oscillatory Schemes

doi:10.1007/s10915-019-01042-w

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	Modified Stencil Approximations for Fifth-Order Weighted Essentially Non-oscillatory Schemes
	Wang, Yahui 1,2,3; Du, Yulong 4; Zhao, Kunlei 1,2,3; Yuan, Li 1,2,3
	2019-11-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	81 期号:2 页码:898-922
摘要	In this paper, a modified fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme is presented. The quadratic polynomial approximation of numerical flux on each candidate stencil of the traditional WENO-JS scheme is modified by adding a form of cubic terms such that the resulting stencil approximation achieves fourth-order accuracy. And the corresponding smoothness indicators are calculated. The modified candidate fluxes and local smoothness indicators, when used in the WENO-JS scheme, can make the resulting new scheme (called WENO-MS) achieve fifth-order convergence in smooth regions including first-order critical points. A series of one- and two-dimensional numerical examples are presented to demonstrate the performance of the new scheme. The numerical results show that the proposed WENO-MS scheme provides a comparable or higher resolution of fine structures compared with the WENO-M, WENO-Z and P-WENO schemes, while it increases only 7% of CPU time compared with the traditional WENO-JS scheme.
关键词	WENO scheme Stencil approximation order Smoothness indicator Hyperbolic conservation law Euler equation
DOI	10.1007/s10915-019-01042-w
收录类别	SCI
语种	英语
资助项目	Natural Science Foundation of China[11261160486] ; Natural Science Foundation of China[91641107] ; Natural Science Foundation of China[91852116] ; Fundamental Research of Civil Aircraft[MJ-F-2012-04]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000491440200011
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50706
专题	中国科学院数学与系统科学研究院
通讯作者	Yuan, Li
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China 4.Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China
推荐引用方式 GB/T 7714	Wang, Yahui,Du, Yulong,Zhao, Kunlei,et al. Modified Stencil Approximations for Fifth-Order Weighted Essentially Non-oscillatory Schemes[J]. JOURNAL OF SCIENTIFIC COMPUTING,2019,81(2):898-922.
APA	Wang, Yahui,Du, Yulong,Zhao, Kunlei,&Yuan, Li.(2019).Modified Stencil Approximations for Fifth-Order Weighted Essentially Non-oscillatory Schemes.JOURNAL OF SCIENTIFIC COMPUTING,81(2),898-922.
MLA	Wang, Yahui,et al."Modified Stencil Approximations for Fifth-Order Weighted Essentially Non-oscillatory Schemes".JOURNAL OF SCIENTIFIC COMPUTING 81.2(2019):898-922.