Mitra Vizheh - Department of Mathematics, Shahed University, Tehran, P.O. Box: ۱۸۱۵۱-۱۵۹, Iran
Syaed Hodjatollah Momeni-Masuleh - Department of Mathematics, Shahed University, Tehran, P.O. Box: ۱۸۱۵۱-۱۵۹, Iran
Alaeddin Malek - Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, P.O. Box: ۱۴۱۱۵-۱۳۴, Iran

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the optimal control of the Navier-Stokes equations is proposed. Numerical examples are given to demonstrate the efficiency of the method.

Optimal Control Problems, Navier-Stokes equations, PDE-constrained optimization, quasi-Newton algorithm, Finite difference