Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-13T05:08:19.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical Problems in Transonic Flow

Published online by Cambridge University Press:  20 November 2018

Cathleen Synge Morawetz
Cathleen Synge Morawetz*
Affiliation:
Courant Institute of Mathematical Sciences, New YorkN.Y. 10012.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We present an outline of the problem of irrotational compressible flow past an airfoil at speeds that lie somewhere between those of the supersonic flight of the Concorde and the subsonic flight of commercial airlines. The problem is simplified and the important role of modifying the equations with physics terms is examined.

Keywords

35XX35M0576XX76H05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 2 , 01 June 1986 , pp. 129 - 139
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Bauer, F., Garabedian, P., and Korn, D., A theory of supercritical wing sections with computer programs and examples, Lecture Notes in Econom. and Math. Syst., vol. 66, Springer-Verlag, Berlin and New York, 1972. See also with A. Jameson, II, 108, same series and III, 150, same series.Google Scholar
2. Busemann, A., Wider stand bei geschwindigkeiten naher der schallgeschwindigkeiten, Proc. Third Internat. Congr. Appl. Mewch. 1 (1930), 282–285.Google Scholar
3. DiPernaR., J., Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal. 82 (1983) 27–70.Google Scholar
4. Glimm, J., and LaxP., D., Decay of solutions of systems of nonlinear hyperbolic conservation lawsy Memoirs AMS, #101, 1979.Google Scholar
5. Goodman, J., Thesis, to appear as a paper.Google Scholar
6. Jameson, A., Iterative solution of transonic flow over airfoils and wings including flows at Math I, Comm. Pure Appl. Math. 27 (1974) 283–309.Google Scholar
7. KacprzynskiJ., J., OhmanL., H., GarabedianP., R., and KornD., G., National Research Council of Canada, Aeronautical Report LR-554.Google Scholar
8. LighthillM., J., On the hodograph transformation for high-speed flow. II. A flow with circulation. Quart. J. Mech. Appl. Math. 1 (1948), 442–450. The hodograph transformation in transonic flow. Ill, Flow around a body, Proc. Roy. Soc. London Ser. A 191 (1947), 341-369.Google Scholar
9. Magnus, R., and Yoshihara, H., Inviscid transonic flow over airfoils, AIAA Jour. 8 (1970), 2157–2162.Google Scholar
10. MorawetzC., S., On a weak solution for a transonic flow problem, to appear in CPAM.Google Scholar
11. MorawetzC., S., On the nonexistence of continuous transonic flows past profiles. I, Comm. Pure Appl. Math. 9 (1956), 45–68. II, 10 (1975), 107-132. III 11 (1958), 129-144. See also 17 (1964), 357-367.Google Scholar
12. F., Murât, Compacité par compensation, Ann. Scuola Norm. Sup. Pisa 5 (1978) 489–507.Google Scholar
13. MurmanE., M., and ColeJ., D., Calculation of plane steady transonic flows, A. I. A. A. Journal 9 (1971), 114–121.Google Scholar
14. TartarL., C., Compensated compactness and applications to partial differential equations, Nonlinear Analysis and Mechanics, Heriot-Watt Symp. IV, (1979) 136–192. Research Notes in Mathematics, Pitman.Google Scholar