Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T06:32:13.384Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.