On the identification of a rigid body immersed in a fluid: A numerical approach

This work deals with the study of an inverse geometric problem in fluid mechanics. In particular, we are interested in the numerical reconstruction of a rigid body which is immersed in a cavity, filled with a fluid, by means of measurements of the Cauchy forces and the velocity of the fluid on one part of the exterior boundary. This problem was studied in [Alvarez C, Conca C, Friz L, Kavian L, Ortega JH. Identification of immersed obstacles via boundary measurements. Inverse Problems 2005; 21:1531–52], where the authors proved the identifiability and stability for this problem. In this work we present a numerical method for the reconstruction of the rigid body for some particular geometries.