| 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
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| Corresponding Author | Shen, Yiqing([email protected]) |
| Source Publication | JOURNAL OF SCIENTIFIC COMPUTING
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| 2019-12-01 | |
| Volume | 81Issue:3Pages:1732-1766 |
| ISSN | 0885-7474 |
| Abstract | First 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. |
| Keyword | Third-order WENO scheme Discontinuity-detecting method Non-nodal critical point Hybrid-WENO scheme |
| DOI | 10.1007/s10915-019-01060-8 |
| Indexed By | SCI ; EI |
| Language | 英语 |
| WOS ID | WOS:000516825700002 |
| WOS Keyword | ESSENTIALLY NONOSCILLATORY SCHEMES ; EFFICIENT IMPLEMENTATION ; HIGH-ORDER |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| Funding Project | NKRDPC[2016YFA0401200] ; NSAF[U1530145] ; NSFC[11872067] ; NSFC[91852203] ; SCP[TZ2016002] |
| Funding Organization | NKRDPC ; NSAF ; NSFC ; SCP |
| Classification | 一类 |
| Ranking | 1 |
| Contributor | Shen, Yiqing |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/81626 |
| Collection | 高温气体动力学国家重点实验室 |
| Affiliation | 1.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.Rp_Au:Shen, Yiqing |
| 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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| Jp2020007.pdf（2840KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | View Download | |
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