Topological asymptotic formula for the 3D non-stationary Stokes problem and application

Maatoug Hassine (1) , Rakia Malek (1)

1 FSM - Faculté des Sciences de Monastir

This paper is concerned with a topological asymptotic expansion for a parabolic operator. We consider the three dimensional non-stationary Stokes system as a model problem and we derive a sensitivity analysis with respect to the creation of a small Dirich-let geometric perturbation. The established asymptotic expansion valid for a large class of shape functions. The proposed analysis is based on a preliminary estimate describing the velocity field perturbation caused by the presence of a small obstacle in the fluid flow domain. The obtained theoretical results are used to built a fast and accurate detection algorithm. Some numerical examples issued from a lake oxygenation problem show the efficiency of the proposed approach.

Mots clés: Topological asymptotic expansion; calculus of variations; non-stationary Stokes system; topology optimization; lake oxygenation problem

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

Maatoug Hassine, Rakia Malek. Topological asymptotic formula for the 3D non-stationary Stokes problem and application. 2018. ⟨hal-01851477v1⟩