Active Control and Drag Optimization for Flow Past a Circular Cylinder: I. Oscillatory Cylinder Rotation

The main objective of this article is to investigate computational methods for the active control and drag optimization of incompressible viscous flow past cylinders, using the two-dimensional Navier–Stokes equations as the flow model. The computational methodology relies on the following ingredients: space discretization of the Navier–Stokes equations by finite element approximations, time discretization by a second-order-accurate two-step implicit/explicit finite difference scheme, calculation of the cost function gradient by the adjoint equation approach, and minimization of the cost function by a quasi-Newton method à la BFGS. The above methods have been applied to boundary control by rotation of the flow around a circular cylinder and show 30 to 60% drag reduction, compared to the fixed cylinder configuration, for Reynolds numbers in the range from 200 to 1000.