On the detection of several obstacles in 2d stokes flow: topological sensitivity and combination with shape derivatives

Abstract

We consider the inverse problem of detecting the location and the shape of several obstacles immersed in a uid owing in a larger bounded domain from partial boundary measurements in the two dimensional case. The uid ow is governed by the steady-state Stokes equations. We use a topological sensitivity analysis for the Kohn-Vogelius functional in order to nd the number and the qualitative location of the objects. Then we explore the numerical possibilities of this approach and also present a numerical method which combines the topological gradient algorithm with the classical geometric shape gradient algorithm; this blending method allows to nd the number of objects, their relative location and their approximate shape.