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Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede pp 205–211Cite as

Use of optimal control theory for the numerical simulation of transonic flow by the method of finite elements

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Part of the book series: Lecture Notes in Physics ((LNP,volume 59))

Abstract

It is shown that the transonic equation for compressible potential flow is equivalent to an optimal control problem of a linear distributed parameter system. This problem can be discretized by the finite element method and solved by a conjugate gradient algorithm. Thus a new class of methods for solving the transonic equation is obtained. Il is particularly well adapted to problems with complicate two or three dimensional geometries and shocks.

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References

  • GARABEDIAN P.R.; KORN D.G.-“Numerical design of transonic airfoils Academic Press, New York 1971.

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  • GELDER D. Solution of the compressible flow equation. Int. J. on Num. Meth. in Eng., Vol. 3, pp. 35–43 (1971).

    Article  MATH  Google Scholar 

  • JAMESON A. Iterative solution of transonic flows. Conf. Pure and applied Math. (1974).

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  • LIONS J.L. “Optimal control of distributed systems” Springer 1969

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  • NORRIES D.H., G. DE VRIES-The finite element method Academic Press 1973

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  • PERIAUX J. Three dimensional analysis of compressible potential flows with the finite element method. Int. J. for Num. Methods in Eng., Vol. 9 (1975).

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Author information

Authors and Affiliations

  1. PARIS VI, Quai St-Bernard, 75006, Paris

    R. Glowinski

  2. AMD-BA, 78 quai Carnot, 92210, St-Cloud

    J. Periaux

  3. IRIA, Domaine de Voluceau Rocquencourt, 78150, Le Chesnay

    O. Pironneau

Authors
  1. R. Glowinski
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  2. J. Periaux
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  3. O. Pironneau
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Editor information

Adriaan I. van de Vooren Pieter J. Zandbergen

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© 1979 Springer-Verlag

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Glowinski, R., Periaux, J., Pironneau, O. (1979). Use of optimal control theory for the numerical simulation of transonic flow by the method of finite elements. In: van de Vooren, A.I., Zandbergen, P.J. (eds) Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28 – July 2, 1976 Twente University, Enschede. Lecture Notes in Physics, vol 59. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-08004-X_318

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  • DOI: https://doi.org/10.1007/3-540-08004-X_318

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08004-6

  • Online ISBN: 978-3-540-37548-7

  • eBook Packages: Springer Book Archive

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