Optimization with the time-dependent Navier-Stokes equations as constraints

Document Type : Research Paper


1 Department of Mathematics, Shahed University, Tehran, P.O. Box: 18151-159, Iran

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, P.O. Box: 14115-134, 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.