Geometric inverse problem for the nonstationary Stokes equations using topological sensitivity analysis

Abstract

We study in this paper a geometric inverse problem in fluid mechanics. The goal is to determine the location of an object in the fluid domain from boundary information. We consider the case of a nonstationary two‐dimensional Stokes flow. Our approach is based on the Kohn–Vogelius concept and the topological gradient method. We develop a new topological asymptotic expansion, which can be used as a basic step for developing accurate detection algorithms.