NUMERICAL-SOLUTION OF A FLOW-CONTROL PROBLEM - VORTICITY REDUCTION BYDYNAMIC BOUNDARY ACTION

In order to laminarize an unsteady, internal flow, the vorticity field is minimized, in a least-squares sense, using an optimal-control appr oach. The flow model is the Navier-Stokes equation for a viscous incom pressible fluid, and the flow is controlled by suction and blowing on a part of the boundary. A quasi-Newton method is used for the minimiza tion of a quadratic objective function involving a measure of the vort icity and a regularization term. The Navier-Stokes equations are appro ximated using a finite-difference scheme in time and finite-element ap proximations in space. Accurate expressions for the gradient of the di screte objective function are needed to obtain a satisfactory converge nce rate of the minimization algorithm. Therefore, first-order necessa ry conditions for a minimizer of the objective function are derived in the fully discrete case. A memory-saving device is discussed without which problems of any realistic size, especially in three space dimens ions, would remain computationally intractable. The feasibility of the optimal-control approach for ow-control problems is demonstrated by n umerical experiments for a two-dimensional flow in a rectangular cavit y at a Reynolds number high enough for nonlinear effects to be importa nt.