A reduced order method for control of fluid flows

This article presents a reduced order method for simulation and control of fluid flows. The major advantage of this method over others, such as finite element, finite difference or spectral method is that it has fewer degrees of freedom. The present methodology's feasibility for flow control is demonstrated on two boundary control problems. The first one is a velocity tracking problem in cavity flow and the second one is a vorticity control problem in channel flow. We cast the control problems as constrained minimization problem and compute the control by applying Newton like methods to the necessary conditions of optimality. Our computational experiments indicate some promises of the proposed reduced order model.