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High order weighted essentially nonoscillatory WENO-eta schemes for hyperbolic conservation laws
Alternative TitleJ. Comput. Phys.
Fan, Ping1,2
2014-07-15
Source PublicationJOURNAL OF COMPUTATIONAL PHYSICS
ISSN0021-9991
Volume269Issue:1Pages:355-385
AbstractIn [8], the authors have designed a new fifth-order WENO finite-difference scheme (named WENO-eta) by introducing a new local smoothness indicator which is defined based on the Lagrangian interpolation polynomials and has a more succinct form compared with the classical one proposed by Jiang and Shu [12]. With this new local smoothness indicator, higher order global smoothness indicators were able to be devised and the corresponding scheme (named WENO-Z eta) displayed less numerical dissipations than the classic fifth-order WENO schemes, including WENO-JS [12] and WENO-Z [5,6]. In this paper, a close look is taken at Taylor expansions of the Lagrangian interpolation polynomials of the WENO sub-stencils and the related inherited symmetries of the local smoothness indicators, which allows the extension of the WENO-eta scheme to higher orders of accuracy. Furthermore, general formulae for the global smoothness indicators are derived with which the WENO-Z eta schemes can be extended to all odd-orders of accuracy. Numerical experiments are conducted to demonstrate the performance of the proposed schemes. (C) 2014 Elsevier Inc. All rights reserved.; In [8], the authors have designed a new fifth-order WENO finite-difference scheme (named WENO-eta) by introducing a new local smoothness indicator which is defined based on the Lagrangian interpolation polynomials and has a more succinct form compared with the classical one proposed by Jiang and Shu [12]. With this new local smoothness indicator, higher order global smoothness indicators were able to be devised and the corresponding scheme (named WENO-Z eta) displayed less numerical dissipations than the classic fifth-order WENO schemes, including WENO-JS [12] and WENO-Z [5,6]. In this paper, a close look is taken at Taylor expansions of the Lagrangian interpolation polynomials of the WENO sub-stencils and the related inherited symmetries of the local smoothness indicators, which allows the extension of the WENO-eta scheme to higher orders of accuracy. Furthermore, general formulae for the global smoothness indicators are derived with which the WENO-Z eta schemes can be extended to all odd-orders of accuracy. Numerical experiments are conducted to demonstrate the performance of the proposed schemes. (C) 2014 Elsevier Inc. All rights reserved.
KeywordWeighted Essentially Non-oscillatory Weno-z Weno-eta Weno-z Eta Smoothness Indicators High Order Accuracy
SubtypeArticle
WOS HeadingsScience & Technology ; Technology ; Physical Sciences
DOI10.1016/j.jcp.2014.03.033
URL查看原文
Indexed BySCI
Language英语
WOS KeywordEFFICIENT IMPLEMENTATION ; MESHES
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000335439300020
Citation statistics
Cited Times:8[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Version出版稿
Identifierhttp://ir.ipe.ac.cn/handle/122111/10899
Collection研究所(批量导入)
Affiliation1.Chinese Acad Sci, Inst Proc Engn, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Inst Mech, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Fan, Ping. High order weighted essentially nonoscillatory WENO-eta schemes for hyperbolic conservation laws[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2014,269(1):355-385.
APA Fan, Ping.(2014).High order weighted essentially nonoscillatory WENO-eta schemes for hyperbolic conservation laws.JOURNAL OF COMPUTATIONAL PHYSICS,269(1),355-385.
MLA Fan, Ping."High order weighted essentially nonoscillatory WENO-eta schemes for hyperbolic conservation laws".JOURNAL OF COMPUTATIONAL PHYSICS 269.1(2014):355-385.
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