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On optimum profiles in Stokes flow

Published online by Cambridge University Press:  29 March 2006

O. Pironneau
O. Pironneau
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

In this paper, we obtain the first-order necessary optimality conditions of an optimal control problem for a distributed parameter system with geometric control, namely, the minimum-drag problem in Stokes flow (flow at a very low Reynolds number). We find that the unit-volume body with smallest drag must be such that the magnitude of the normal derivative of the velocity of the fluid is constant on the boundary of the body. In a three-dimensional uniform flow, this condition implies that the body with minimum drag has the shape of a pointed body similar in general shape to a prolate spheroid but with some differences including conical front and rear ends of angle 120°.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 1 , 5 June 1973 , pp. 117 - 128
Copyright
© 1973 Cambridge University Press

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References

Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Ladyzhenskaya, O. 1963 The Mathematical Theory of Viscous Incompressible Flow. Gordon & Breach.
Lattes, R. & Lions, J. L. 1969 The Method of Quasi-Reversibility. Elsevier.
Lions, J. L. 1968 Contrôle Optimal de Systèmes Gouvernés par des Equations aux Derivées Partielles. Paris: Dunod.
Lions, J. L. 1972 Some aspects of the optimal control of distributed parameter systems. Regional Conf. in Appl. Math., Philadelphia SIAM.Google Scholar
Lions, J. L. & Magenes, E. 1967 Problèmes aux Limites Non-homogènes, vol. 1. Paris: Dunod.
Polak, E. 1971 Computational Methods in Optimisation. Academic.
Tuck, E. O. 1968 Proc. Conf. Hydraul. Fluid Mech. p. 29. Australia: Institute of Engineers.
Watson, S. R. 1971 J. Inst. Math. Applics. 7, 367–376.