Application of optimal control theory to transonic flow computations by finite element methods

  • M. O. Bristeau
Aeronatical Fluid Mechanics and Transonic Flows
Part of the Lecture Notes in Physics book series (LNP, volume 91)


We apply optimal control theory to the solution of the transonic potential flow equation. The problem is discretized by the finite element method ; the entropy condition is treated as a constraint or by the addition of an artificial viscosity to the equation.


Mach Number Pressure Coefficient Finite Difference Scheme Optimal Control Theory Entropy Condition 
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  1. BAUER F., GARABEDIAN P., KORN D. [1] Supercritical Wing Sections, Lecture Notes in Economics and Math. Systems, Vol., Springer Verlag, 1972.Google Scholar
  2. CIARLET P.G., RAVIART P.A. [1] A mixed finite element method for the biharmonic equation, in Mathematical Aspects of finite elements in partial differential equations. 'C. de Boor., Acad. Press, 1974, 125–145.Google Scholar
  3. FORTIN M. [1] Résolution Numérique des Equations de Navier-Stokes par des éléments finis de type mixte. Rapport de recherche LABORIA-IRIA No 184, Juillet 1976.Google Scholar
  4. GLOWINSKI R. [1] Approximation externe par éléments finis d'ordre un et deux du problème de Dirichlet pour Δ2. In Topics in Numerical Analysis, J.J.H. Miller Ed., Acad. Press, (1973), pp. 123Google Scholar
  5. GLOWINSKI R., PERIAUX J., PIRONNEAU O. [1] Transonic flow simulation by the finite element method via optimal control. Proceedings of the Second International Symposium in Flow Problems, Santa Margherita (Italy), June, pp. 249–259Google Scholar
  6. H−1 Least squares for non-linear P.D.E.: Applications to incompressible viscous flows and to transonic flows. Proceedings of the International Meeting on Finite Elements for Non Elliptic Problems, Tel Aviv, July 1977, N. Geffen Ed.Google Scholar
  7. GLOWINSKI R., PIRONNEAU O. [1] Calcul d'écoulements transsoniques par des méthodes d'éléments finis et de contrôle optimal. In Computing Methods in Allied Sciences and Engineering, R. Glôwinski, J.L. Lions Ed., Lecture Notes in Economics an Mathematical Systems, Vol. 134, Springer, 1976, pp. 276–296.Google Scholar
  8. On the computation of transonic flows, Proceedings of the first Franco-Japonese Colloquium on Functional and Numerical Analysis, Tokyo, Kyoto, September 1976.Google Scholar
  9. Least square solution of non linear problems in Fluid Dynamics. Proceedings of Simposo Internacional em Macanica do Continuo e Equaçoes Diferenciais Parciais, Rio de Janeiro, Agosto de 1977.Google Scholar
  10. JAMESON A, [1] Transonic flow calculations. In Proceedings of Conference on Computational Fluid Dynamics, Von Karman Institute, March 1976, Brussels (Belgium).Google Scholar
  11. JAMESON A., CAUGHEY D.A. [1] A finite volume method for transonic potential flow calculations. AIAA Journal, 1977.Google Scholar
  12. LANDAU L., LIFCHITZ F. [1] Mécanique des Fluides, Edition MIR, Moscou, 1953Google Scholar
  13. LESAINT P. [1] Sur la résolution des sytèmes hyperboliques du premier ordre par des méthodes d'éléments finis. Thèse, Paris, 1975.Google Scholar
  14. LIONS J.L. [1] Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, Dunod, 1968.Google Scholar
  15. Murman, E. M. and Cole, J. D., Calculation of plane steady transonic flows, AIAA J., Vol. 9, 1971, pp. 114–121.Google Scholar
  16. PERIAUX J., PIRONNEAU O. [1] Optimal control formulation for non linear P.D.E. and applications to transonic inviscid flows and to incompressible viscous flows. To appear in Proceedings of the Conference on Numerical Methods in Applied Fluid Dynamics, Reading, January 1978.Google Scholar
  17. POLAK E. [1] Computational Methods in Optimization. Acad. Press, 1971.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • M. O. Bristeau
    • 1
  1. 1.IRIA-LABORIA Domaine de VoluceauRocquencourtLe Chesnay

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