Kohn-Vogelius formulation and high-order topological asymptotic formula for identifying small obstacles in a fluid medium

Abstract This paper concerns the identification of a small obstacle immersed in a Stokes flow from boundary measurements. The proposed approach is based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. We derive a high order asymptotic formula describing the variation of a Kohn-Vogelius type functional with respect to the insertion of a small obstacle inside the fluid flow domain. The obtained asymptotic formula will serve as very useful tools for developing accurate and robust numerical reconstruction algorithms.