Suppression of vortex shedding for ow around a circular cylinder using optimal control

Adjoint formulation is employed for the optimal control of ow around a rotating cylinder, governed by the unsteady Navier–Stokes equations. The main objective consists of suppressing Karman vortex shedding in the wake of the cylinder by controlling the angular velocity of the rotating body, which can be constant in time or time-dependent. Since the numerical control problem is ill-posed, regularization is employed. An empirical logarithmic law relating the regularization coe?cient to the Reynolds number was derived for 606Re6140. Optimal values of the angular velocity of the cylinder are obtained for Reynolds numbers ranging from Re=60 to Re=1000. The results obtained by the computational optimal control method agree with previously obtained experimental and numerical observations. A signiAcant reduction of the amplitude of the variation of the drag coe?cient is obtained for the optimized values of the rotation rate. Copyright ? 2002 John Wiley & Sons, Ltd.