Topological asymptotic expansion for the full Navier–Stokes equations

Article type: Research Article

Authors: Hassine, Maatoug^{; *} | Chaouch, Sana

Affiliations: FSM, Monastir University, Tunisie

Correspondence: [*] Corresponding author. E-mail: maatoug.hassine@enit.rnu.tn.

Abstract: This paper is concerned with a topological sensitivity analysis for the two dimensional incompressible Navier–Stokes equations. We derive a topological asymptotic expansion for a shape functional with respect to the creation of a small geometric perturbation inside the fluid flow domain. The geometric perturbation is modeled as a small obstacle. The asymptotic behavior of the perturbed velocity field with respect to the obstacle size is discussed. The obtained results are valid for a large class of shape fonctions and arbitrarily shaped geometric perturbations. The established topological asymptotic expansion provides a useful tool for shape and topology optimization in fluid mechanics.

Keywords: Asymptotic expansion, topological sensitivity analysis, Navier–Stokes equations, nonlinear operator, topological gradient, fluid mechanics, topology optimization

DOI: 10.3233/ASY-221807

Journal: Asymptotic Analysis, vol. 133, no. 1-2, pp. 91-121, 2023