Optimal shape design for the time‐dependent Navier–Stokes flow

This paper is concerned with the problem of shape optimization of two‐dimensional flows governed by the time‐dependent Navier–Stokes equations. We derive the structures of shape gradients for time‐dependent cost functionals by using the state derivative and its associated adjoint state. Finally, we apply a gradient‐type algorithm to our problem, and numerical examples show that our theory is useful for practical purposes and the proposed algorithm is feasible in low Reynolds number flows. Copyright © 2007 John Wiley & Sons, Ltd.