Topological sensitivity analysis for the 3D nonlinear Navier–Stokes equations

Article type: Research Article

Authors: Hassine, Maatoug^{; *} | Ouni, Marwa

Affiliations: Faculté des sciences de Monastir, Monastir University, Monastir, Tunisia

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

Abstract: This work is devoted to a topological asymptotic expansion for the nonlinear Navier–Stokes operator. We consider the 3D Navier–Stokes equations as a model problem and we derive a topological sensitivity analysis for a design function with respect to the insertion of a small obstacle inside the fluid flow domain. The asymptotic behavior of the perturbed velocity field with respect to the obstacle size is examined. The performed mathematical framework can be applied for a large class of design functions and arbitrarily shaped geometric perturbations. The obtained asymptotic formula can serve as a useful tool for solving a variety of topology optimization problems in fluid mechanics.

Keywords: Topological asymptotic expansion, 3D Navier–Stokes equations, analysis of sensitivity, topological gradient based methods, fluid mechanics

DOI: 10.3233/ASY-231855

Journal: Asymptotic Analysis, vol. 135, no. 1-2, pp. 277-304, 2023