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Supersonic flow onto solid wedges, multidimensional shock waves and free boundary problems
Chen, Gui-Qiang1,2,3,4
2017-08-01
Source PublicationSCIENCE CHINA-MATHEMATICS
ISSN1674-7283
Volume60Issue:8Pages:1353-1370
AbstractWhen an upstream steady uniform supersonic flow impinges onto a symmetric straight-sided wedge, governed by the Euler equations, there are two possible steady oblique shock configurations if the wedge angle is less than the detachment angle-the steady weak shock with supersonic or subsonic downstream flow (determined by the wedge angle that is less than or greater than the sonic angle) and the steady strong shock with subsonic downstream flow, both of which satisfy the entropy condition. The fundamental issue-whether one or both of the steady weak and strong shocks are physically admissible solutions-has been vigorously debated over the past eight decades. In this paper, we survey some recent developments on the stability analysis of the steady shock solutions in both the steady and dynamic regimes. For the static stability, we first show how the stability problem can be formulated as an initial-boundary value type problem and then reformulate it into a free boundary problem when the perturbation of both the upstream steady supersonic flow and the wedge boundary are suitably regular and small, and we finally present some recent results on the static stability of the steady supersonic and transonic shocks. For the dynamic stability for potential flow, we first show how the stability problem can be formulated as an initial-boundary value problem and then use the self-similarity of the problem to reduce it into a boundary value problem and further reformulate it into a free boundary problem, and we finally survey some recent developments in solving this free boundary problem for the existence of the Prandtl-Meyer configurations that tend to the steady weak supersonic or transonic oblique shock solutions as time goes to infinity. Some further developments and mathematical challenges in this direction are also discussed.
Keywordshock wave free boundary wedge problem transonic mixed type Euler equations static stability dynamic stability
DOI10.1007/s11425-016-9045-1
Language英语
Funding ProjectUS National Science Foundation[DMS-0935967] ; US National Science Foundation[DMS-0807551] ; UK Engineering and Physical Sciences Research Council[EP/E035027/1] ; UK Engineering and Physical Sciences Research Council[EP/L015811/1] ; National Natural Science Foundation of China[10728101] ; Royal Society-Wolfson Research Merit Award (UK)
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000405622500001
PublisherSCIENCE PRESS
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26112
Collection中国科学院数学与系统科学研究院
Affiliation1.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.Univ Oxford, Math Inst, Oxford OX2 6GG, England
Recommended Citation
GB/T 7714
Chen, Gui-Qiang. Supersonic flow onto solid wedges, multidimensional shock waves and free boundary problems[J]. SCIENCE CHINA-MATHEMATICS,2017,60(8):1353-1370.
APA Chen, Gui-Qiang.(2017).Supersonic flow onto solid wedges, multidimensional shock waves and free boundary problems.SCIENCE CHINA-MATHEMATICS,60(8),1353-1370.
MLA Chen, Gui-Qiang."Supersonic flow onto solid wedges, multidimensional shock waves and free boundary problems".SCIENCE CHINA-MATHEMATICS 60.8(2017):1353-1370.
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