Topological sensitivity analysis based method for solving a geometry reconstruction problem

This paper is concerned with the topological sensitivity analysis for a parabolic type operator. We consider the unsteady-state heat transfer equation as a model problem and we develop the topological asymptotic expansion valid for a large class of cost functions. The obtained theoretical results are based on a simplified mathematical analysis involving the elliptic part of the operator. In the numerical part, we proposed a simple and fast geometry reconstruction algorithm. The proposed algorithm is applied for recovering internal cooling holes in a turbine blade by minimizing various error functions measuring the difference between the current and actual temperature fields.