Unsteady flow optimization by a stabilized finite element method

Abstract

SUMMARYThis 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.