Shock Optimization for Airfoil Design Problems

  • Olivier Pironneau
Conference paper
Part of the Springer Optimization and Its Applications book series (SOIA, volume 33)


We begin by recalling the classical approach to solve shape design problems by gradient methods. Then we proceed to explain how automatic differentiation can simplify the analysis and illustrate this approach to a shape design problem where the shock is required to be at a certain place. The object of this chapter is to show that automatic differentiation seems to work even though the gradients and the calculus of variation have to be extended by Distribution theory.


Mach Number Dirac Masse Automatic Differentiation NACA Airfoil Transonic Speed 
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    B. Mohammadi and O. Pironneau: Applied Numerical Optimal Shape Design. Oxford U. Press. (2001).Google Scholar
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    A. Caughey and M. Hafez (ed.): Pros and Cons of Airfoil Optimization, Frontier of Computational Fluid Dynamics, World Scientific, Singapore. (1998).Google Scholar
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    C. Bardos and O. Pironneau : Derivatives and Control in the Presence of Shocks. Computational Fluid Dynamics Journal, vol 12, no.1 (April 2003).Google Scholar

Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.LJLL, University of Paris VI & IUFFrance

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