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In this paper, we deal with topology optimization attributed to the non stationary Navier-Stokes equations. We propose an approach where we analyze the sensitivity of a shape function relating to a perturbation of the flow domain. A numerical optimization algorithm based on topological gradient method is built and applied to the 2D Tesla micro valve reconstruction. Some numerical results confirm the efficiency of the proposed approach.

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We consider the geometric inverse problem of determining an immersed obstacle in a two-dimensional non-stationary Stokes fluid flow. We use the topological gradient method to solve this problem. The unknown obstacle is located and reconstructed using the leading term of the Khon-Vogelius shape function variation. We propose a simple and fast detection algorithm. The efficiency and accuracy of the proposed approach are illustrated by some numerical examples.