the millions. Conventional optimization approaches prove inadequate for such large-scale optimization problems.
The focus of this work is on the development of large-scale numerical optimization methods for optimal control of steady incompress-
The development of numerical optimization methods ible Navier-Stokes flows. The control is affected by the suction or for optimal flow control is built on a mathematical foundainjection of fluid on portions of the boundary, and the objective tion that continues to be enlarged. A number of basic function represents the rate at which energy is dissipated in the fluid. results concerning existence and regularity of solutions to
We develop reduced Hessian sequential quadratic programming the continuous problem, as well as error estimates for its methods that avoid converging the flow equations at each iteration.
numerical approximation, have been established mostly
Both quasi-Newton and Newton variants are developed and compared to the approach of eliminating the flow equations and variover the last decade; see the article by Gunzburger et al.
ables, which is effectively the generalized reduced gradient method.
for a good overview [13].
Optimal control problems are solved for two-dimensional flow
This rich mathematical basis, the increasing power of around a cylinder and three-dimensional flow around a sphere. The computers, and the maturation of numerical methods for examples demonstrate at least an order-of-magnitude reduction in the flow simulation itself motivate the desire to develop time taken, allowing the optimal solution of flow control problems in as little as half an hour on a desktop workstation. ᮊ 1997 Academic Press numerical optimization methods for solution of optimal flow control problems. The latter forms the subject of this article. Here, we focus on a prototype problem of optimal