The topological asymptotic expansion for the Quasi-Stokes problem

¹ ENIT-LAMSIN & FSM, Campus Universitaire, Le Belvédaire BP 37, 1002 Tunis, Tunisia; maatoug.hassine@enit.rnu.tn.
² Mathématiques pour l'Industrie et la Physique, UMR 5640, Université de Paul Sabatier, 118 route de Narbonne, 31032 Toulouse Cedex 4, France.

Received: 28 August 2002
Revised: 6 November 2003

Abstract

In this paper, we propose a topological sensitivity analysis for the Quasi-Stokes equations. It consists in an asymptotic expansion of a cost function with respect to the creation of a small hole in the domain. The leading term of this expansion is related to the principal part of the operator. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the locations of a fixed number of air injectors in an eutrophized lake.