Shape inverse problem for Stokes-Brinkmann equations

In this paper, we propose an imaging technique for the detection of porous inclusions in a stationary flow governed by Stokes-Brinkmann equations. We introduce the velocity method to perform the shape deformation, and derive the structure of shape gradient for the cost functional based on the continuous adjoint method and the function space parametrization technique. Moreover, we present a gradient-type algorithm to the shape inverse problem. The numerical results demonstrate the proposed algorithm is feasible and effective for the quite high Reynolds numbers problems.