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This paper is concerned with an optimal shape design problem in fluid mechanics. The fluid flow is governed by the Stokes equations. The theoretical analysis and the numerical simulation are discussed in two and three-dimensional cases. 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. An asymptotic expansion is derived for a large class of cost functions using small topological perturbation technique. A fast and accurate numerical algorithm is proposed. The efficiency of the method is illustrated by some numerical examples.

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