Topological asymptotic expansion for the full Navier–Stokes equations

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.