Unsteady flow optimization by a stabilized finite element method

Abstract

AbstractThis paper presents the problem of shape optimization of two‐dimensional viscous flow governed by the time‐dependent Navier–Stokes equations. The minimization problem of the viscous dissipated energy was established in the fluid domain. The discretization of Navier–Stokes equations is accomplished using a new stabilized finite element method in space and finite difference in time. This new method does not need a stabilization parameter or calculation of high‐order derivatives. We derive the structures of the discrete Eulerian derivative of the cost functional by a discrete adjoint method with a function space parametrization technique. A gradient‐type optimization algorithm with a mesh adaptation technique and a mesh moving strategy is effectively implemented. Copyright © 2009 John Wiley & Sons, Ltd.