Optimal shape design for a time-dependent Brinkman flow using asymptotic analysis techniques

Author:

Dhif R.1,Meftahi H.2,Rjaibi B.1

Affiliation:

1. Laboratory of Mathematical and Numerical Modelling in Engineering Sciences, University of Tunis El-Manar, Tunisia

2. Institute of Computer Science Isikef/University of Jendouba, Tunisia

Abstract

In this paper, we consider the geometric inverse problem of recovering an obstacle ω immersed in a bounded fluid flow Ω governed by the time-dependent Brinkman model. We reformulate the inverse problem into an optimization problem using a least squares functional. We prove the existence of an optimal solution to the optimization problem. Then, we perform the asymptotic expansion of the cost function in a simple way using a penalty method. An important advantage of this method is that it avoids the truncation method used in the literature. To reconstruct the obstacle, we propose a fast algorithm based on the topological derivative. Finally, we present some numerical experiments in two- and three-dimensional cases showing the efficiency of the proposed method.

Publisher

IOS Press

Subject

General Mathematics

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