The aim of this work is to optimize an actuator design so that the flow profile at its exit section is as close as possible to a target profile. The method is founded on the penalization and level-set methods to solve direct and inverse problems on Cartesian meshes The optimization process is written and applied both for Stokes and Navier-Stokes flows. The results show that the method can be successfully applied to the non linear problem to improve the flow profile of an actuator even if the target cannot be totally reached.
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