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Abstract and Applied Analysis
Volume 2014, Article ID 923016, 9 pages
Research Article

Topology Optimization of Time Dependent Viscous Incompressible Flows

1Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia
2Department of Mathematics, College of Sciences of Monastir, Monastir 5000, Tunisia

Received 14 November 2013; Accepted 18 February 2014; Published 24 March 2014

Academic Editor: Bessem Samet

Copyright © 2014 Mohamed Abdelwahed and Maatoug Hassine. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we consider topology and shape optimization problem related to the nonstationary Navier-Stokes system. The minimization of dissipated energy in the fluid flow domain is discussed. The proposed approach is based on a sensitivity analysis of a design function with respect to the insertion of a small obstacle in the fluid flow domain. Some numerical results show the efficiency and accurate of the proposed approach.