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Abstract

The feasibility of finite element and mathematical programming methods for finding an optimal shape for an symmetric airfoil in case of transonic flow is studied. The state problem is solved using multigrid-technique. Numerical examples are given.

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References

  1. F. Angrand, Optimum design for potential flows, Int. J. Num. Meth. Fluids 3 (1983), 265–282.

    Article  Google Scholar 

  2. H. Berger, G. Warnecke and W. Wendland, A convergent finite element formulation for transonic flow, Numerical Methods for Partial Differential Equations 6 (1990), 17–42.

    Article  Google Scholar 

  3. C. de Boor, “A Practical Guide to Splines,” Springer-Verlag, New York, 1978.

    Google Scholar 

  4. V. Braibant and C. Fleury, Shape Optimal Design Using B-splines, Comp. Meth. Appl. Mech. Eng. 44 (1984), 247–267.

    Article  Google Scholar 

  5. V. Danék, Numerical Solution of Transonic Potential Flows with Finite Element Method Using Multigrid Technique, Acta Technica ÒSAV 3 (1986).

    Google Scholar 

  6. V. Danék and F. Marsík, Stability of numerical solution of transonic potential flow,ZAMM, in print.

    Google Scholar 

  7. H. Deconinck and Ch. Hirsch, A multigrid method for the transonic full potential equation discretized with FE on an arbitrary body fitted mesh, Journal of Computational Physics 48 N. 3 (1982), 344–365.

    Article  Google Scholar 

  8. M. Feistauer and J. Neoas, On the solvability of transonic potential flow problems, Z. Anal. Anw. 4 (1985), 305–329.

    Google Scholar 

  9. J. Haslinger and P. Neittaanmäki, “Finite Element Approximation for Optimal Shape Design,” John Wiley & Sons, Chichester, 1988.

    Google Scholar 

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© 1991 Springer Basel AG

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Daněk, V., Mäkinen, R. (1991). Optimal design for transonic flows. In: Neittaanmäki, P. (eds) Numerical Methods for Free Boundary Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 99. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5715-4_10

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  • DOI: https://doi.org/10.1007/978-3-0348-5715-4_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5717-8

  • Online ISBN: 978-3-0348-5715-4

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