This chapter is concerned with the detection of objects immersed in a fluid flow from boundary measurements. To solve the considered geometric inverse problem, we propose an approach based on the Kohn–Vogelius formulation and the topological gradient method. The geometric inverse problem is formulated as a topology optimization one. In the theoretical part, we extend the topological sensitivity analysis method to the parabolic case. We consider the two dimensional non-stationary Stokes system as a model problem, and we derive a topological asymptotic expansion for an energy like shape functional. The established result is based on a preliminary estimate describing the velocity field perturbation caused by the presence of a small obstacle inside the fluid flow. In the numerical part, we propose a simple and fast detection algorithm. The unknown obstacle is located and reconstructed using the leading term of the shape function variation. The efficiency and accuracy of the proposed approach are illustrated by some numerical examples.