Optimal shape design for navier-strokes flow

  • Juan A. Bello
  • Enrique Fernandez-Cara
  • Universidad de Sevilla
  • Jacques Simon
  • C.N.R.S. et Laboratorie de Mathématiques Appliquées
III Optimal Control III.2 Distributed Parameter Systems
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)


The computation of optimal profiles, i.e. those minimizing the drag, has been investigated by several suthors. frequently, the drag has been approximated by the viscous energy which is dissipated in the fluid. For instance, O. Pironneau computes in [9,10] the “derivative” of this quantity adapting Hadamard’s normal variations techniques. F. Murat and J. Simon use in [6] formal calculus to deduce an expression for the derivative. More recently, J. Simon has considered the problem from a rigorous viewpoint in the case of a Stokes flow (cf. [13]). See als [4], for some theoretical and numerical considerations. This paper deals with optimal profiles in Navier-Stokes regime. Let us introduce an initital body Δ and assume that an admissible variation of Δ is represented by a vector field u. We prove that the mapping uJ(Δ+u), where J(Δ+u) is the energy sssociated to the body Δ+u, is Fréchet-differentiable. We also apply some results from [11] to the computation of the derivative.


Total Derivative Stoke Flow Pair Function Formal Calculus Local Derivative 
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Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • Juan A. Bello
    • 1
  • Enrique Fernandez-Cara
    • 1
  • Universidad de Sevilla
  • Jacques Simon
    • 2
  • C.N.R.S. et Laboratorie de Mathématiques Appliquées
  1. 1.Departmento de Análisis MatemáticoUniversidad de SevillaSevillaSpain
  2. 2.Université Blaise Pascal (Clermot-Ferrand 2)Aubiere CedexFrance

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