The topological asymptotic for the Navier-Stokes equations
Mathématiques pour l'Industrie et la Physique, UMR 5640, CNRS-Université Paul Sabatier-INSA, 118 route de Narbonne, 31062 Toulouse Cedex 4, France; email@example.com
Revised: 19 July 2004
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.
Mathematics Subject Classification: 35J60 / 49Q10 / 49Q12 / 76D05 / 76D55
Key words: Shape optimization / topological asymptotic / Navier-Stokes equations.
© EDP Sciences, SMAI, 2005