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In this thesis, we present a continuous adjoint computations approach to shape optimization for unsteady fluid flows. The fluid is described by unsteady incompressible Navier-Stokes equations with slip with friction and penetration with resistance boundary conditions. We present the related adjoint equations. These equations are discretized using a finite element approach. We explain the G2 discretization technique and we examine a mesh adaptivity process based on a goal-oriented error estimator. An optimization algorithm based on conservation of volume is considered. Finally, we give some numerical results.