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The topological asymptotic for the Navier-Stokes equations

Published online by Cambridge University Press:  15 July 2005

Samuel Amstutz
Samuel Amstutz*
Affiliation:
Mathématiques pour l'Industrie et la Physique, UMR 5640, CNRS-Université Paul Sabatier-INSA, 118 route de Narbonne, 31062 Toulouse Cedex 4, France; amstutz@mip.ups-tlse.fr
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Abstract

The aim of the topological asymptotic analysis is to provide an asymptotic expansion of a shape functional with respect to the size of a small inclusion inserted inside the domain. The main field of application is shape optimization. This paper addresses the case of the steady-state Navier-Stokes equations for an incompressible fluid and a no-slip condition prescribed on the boundary of an arbitrary shaped obstacle. The two and three dimensional cases are treated for several examples of cost functional and a numerical application is presented.

Keywords

Shape optimizationtopological asymptoticNavier-Stokes equations.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 3 , July 2005 , pp. 401 - 425
Copyright
© EDP Sciences, SMAI, 2005

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