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On optimum design in fluid mechanics

  • O. Pironneau (a1) (a2)

Abstract

In this paper, the change in energy dissipation due to a small hump on a body in a uniform steady flow is calculated. The result is used in conjunction with the variational methods of optimal control to obtain the optimality conditions for four minimum-drag problems of fluid mechanics. These conditions imply that the unit-area profile of smallest drag has a front end shaped like a wedge of angle 90°.

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Copyright

References

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Finn R.1959 On steady-state solutions of the Navier-Stokes partial differential equations. Arch. Rat. Mech. Anal. 3, 381396.
Heywood J.1970 On stationary solutions of the Navier-Stokes equations as limit of non-stationary solutions. Arch. Rat. Mech. Anal., 37, 4860.
Ladyzhenskaya O.1963 The Mathematical Theory of Viscous Incompressible Flow. Gordon & Breach.
Pironneau O.1973 On optimum profiles in Stokes flow. J. Fluid Mech., 59, 117128.
Pironneau, O. & Polak E.1973 Rate of convergence of a class of methods of feasible directions. SIAM J. Numer. Anal., 10, 161174.
Smith F. T.1973 Laminar flow over a small hump on a flat plate. J. Fluid Mech., 57, 803824.
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On optimum design in fluid mechanics

  • O. Pironneau (a1) (a2)

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