%0 Journal Article %T Optimization with the time-dependent Navier-Stokes equations as constraints %J Computational Methods for Differential Equations %I University of Tabriz %Z 2345-3982 %A Vizheh, Mitra %A Momeni-Masuleh, Syaed Hodjatollah %A Malek, Alaeddin %D 2015 %\ 04/01/2015 %V 3 %N 2 %P 87-98 %! Optimization with the time-dependent Navier-Stokes equations as constraints %K Optimal Control Problems %K Navier-Stokes equations %K PDE-constrained optimization %K quasi-Newton algorithm %K Finite difference %R %X 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. %U https://cmde.tabrizu.ac.ir/article_4484_0de495e641081aae07a2b511ceceb9bf.pdf