IMECH-IR  > 高温气体动力学国家重点实验室
Discontinuity-Detecting Method for a Four-Point Stencil and Its Application to Develop a Third-Order Hybrid-WENO Scheme
Liu SP(刘升平)1,2; Shen YQ(申义庆)1,3
Corresponding AuthorShen, Yiqing(yqshen@imech.ac.cn)
Source PublicationJOURNAL OF SCIENTIFIC COMPUTING
2019-12-01
Volume81Issue:3Pages:1732-1766
ISSN0885-7474
AbstractFirst this paper analyzes the reason for the accuracy losing of the third-order weighted essentially non-oscillatory (WENO) scheme. It is shown that one reason is that the local smoothness indicators of the third-order WENO scheme cannot correctly treat the smooth three-point stencil containing a non-nodal critical point, here, 'non-nodal' means the critical point is not a grid point. And then a discontinuity-detecting method for a four-point stencil is proposed and applied to develop the high order accurate hybrid-WENO scheme by combining the third-order WENO scheme and a third-order upstream scheme. This four-point stencil is actually the stencil used for constructing the third-order WENO scheme (positive and negative numerical fluxes), hence the resulting hybrid-WENO scheme proposed by this paper does not introduce new grid point. Numerical examples show that the detecting method and the hybrid scheme are robust for problems with shocks, and the hybrid scheme obtains real third-order convergence rate for smooth solutions containing critical points.
KeywordThird-order WENO scheme Discontinuity-detecting method Non-nodal critical point Hybrid-WENO scheme
DOI10.1007/s10915-019-01060-8
Indexed BySCI ; EI
Language英语
WOS IDWOS:000516825700002
WOS KeywordESSENTIALLY NONOSCILLATORY SCHEMES ; EFFICIENT IMPLEMENTATION ; HIGH-ORDER
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
Funding ProjectNKRDPC[2016YFA0401200] ; NSAF[U1530145] ; NSFC[11872067] ; NSFC[91852203] ; SCP[TZ2016002]
Funding OrganizationNKRDPC ; NSAF ; NSFC ; SCP
Classification一类
Ranking1
ContributorShen, Yiqing
Citation statistics
Cited Times:10[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/81626
Collection高温气体动力学国家重点实验室
Affiliation1.Chinese Acad Sci, Inst Mech, State Key Lab High Temp Gas Dynam, Beijing 100190, Peoples R China;
2.Beihang Univ, Sch Aeronaut Sci & Engn, Beijing 100191, Peoples R China;
3.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Liu SP,Shen YQ. Discontinuity-Detecting Method for a Four-Point Stencil and Its Application to Develop a Third-Order Hybrid-WENO Scheme[J]. JOURNAL OF SCIENTIFIC COMPUTING,2019,81,3,:1732-1766.
APA 刘升平,&申义庆.(2019).Discontinuity-Detecting Method for a Four-Point Stencil and Its Application to Develop a Third-Order Hybrid-WENO Scheme.JOURNAL OF SCIENTIFIC COMPUTING,81(3),1732-1766.
MLA 刘升平,et al."Discontinuity-Detecting Method for a Four-Point Stencil and Its Application to Develop a Third-Order Hybrid-WENO Scheme".JOURNAL OF SCIENTIFIC COMPUTING 81.3(2019):1732-1766.
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