A Sufficient and Necessary Condition of the Existence of WENO-Like Linear Combination for Finite Difference Schemes

doi:10.4208/cicp.OA-2019-0112

CORC > 力学研究所 > 中国科学院力学研究所 > 高温气体动力学国家重点实验室

	A Sufficient and Necessary Condition of the Existence of WENO-Like Linear Combination for Finite Difference Schemes
	Kang J(康健)1,2; Li XL(李新亮)1,2
刊名	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
	2021-02-01
卷号	29 期号:2 页码:534-570
关键词	Finite difference WENO sufficient and necessary condition proof
ISSN号	1815-2406
DOI	10.4208/cicp.OA-2019-0112
通讯作者	Li, Xinliang(lixl@imech.ac.cn)
英文摘要	In the finite difference WENO (weighted essentially non-oscillatory) method, the final scheme on the whole stencil was constructed by linear combinations of highest order accurate schemes on sub-stencils, all of which share the same total count of grid points. The linear combination method which the original WENO applied was generalized to arbitrary positive-integer-order derivative on an arbitrary (uniform or non-uniform) mesh, still applying finite difference method. The possibility of expressing the final scheme on the whole stencil as a linear combination of highest order accurate schemes on WENO-like sub-stencils was investigated. The main results include: (a) the highest order of accuracy a finite difference scheme can achieve and (b) a sufficient and necessary condition that the linear combination exists. This is a sufficient and necessary condition for all finite difference schemes in a set (rather than a specific finite difference scheme) to have WENO-like linear combinations. After the proofs of the results, some remarks on the WENO schemes and TENO (targeted essentially non-oscillatory) schemes were given.
分类号	一类
资助项目	National Numerical Wind Tunnel project ; National Key Research and Development Program of China[2016YFA0401200] ; National Key Research and Development Program of China[2019YFA0405300] ; NSFC[91852203]
WOS关键词	TARGETED ENO SCHEMES ; ORDER ; SOLVER
WOS研究方向	Physics
语种	英语
WOS记录号	WOS:000596085300008
资助机构	National Numerical Wind Tunnel project ; National Key Research and Development Program of China ; NSFC
其他责任者	Li, Xinliang
内容类型	期刊论文
源URL	[http://dspace.imech.ac.cn/handle/311007/85879]
专题	力学研究所_高温气体动力学国家重点实验室
作者单位	1.Chinese Acad Sci, Inst Mech, State Key Lab High Temp Gas Dynam, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China;
推荐引用方式 GB/T 7714	Kang J,Li XL. A Sufficient and Necessary Condition of the Existence of WENO-Like Linear Combination for Finite Difference Schemes[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2021,29(2):534-570.
APA	康健,&李新亮.(2021).A Sufficient and Necessary Condition of the Existence of WENO-Like Linear Combination for Finite Difference Schemes.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,29(2),534-570.
MLA	康健,et al."A Sufficient and Necessary Condition of the Existence of WENO-Like Linear Combination for Finite Difference Schemes".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 29.2(2021):534-570.