• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.675-691
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• 2002

The focus of this work is on the development of large-scale numerical optimization methods for optimal control of steady incompressible Navier-Stokes flows. The control is affected by the suction or injection of fluid on portions of the boundary, and the objective function of fluid on portions of the boundary, and the objective function represents the rate at which energy is dissipated in the fluid. We develop reduced Hessian sequential quadratic programming. Both quasi-Newton and Newton variants are developed and compared to the approach of eliminating the flow equations and variables, which is effectively the generalized reduced gradient method. Optimal control problems we solved for two-dimensional flow around a cylinder. The examples demonstrate at least an order-of-magnitude reduction in time taken, allowing the optimal solution of flow control problems in as little as half an hour on a desktop workstation.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.661-674
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• 2002

The objective of this study is to develop efficient numerical method to enable solution of optimal control problems of Navier-Stokes flows and to apply these technique to the problem of viscous drag minimization on a bluff body by controlling boundary velocities on the surface of the body. In addition to the industrial importance of the drag reduction problem, it serves as a model for other more complex flow optimization settings, and allows us to study, modify, and improve the behavior of the optimal control methods proposed here. The control is affected by the suction or injection of fluid on portions of the boundary, and the objective function represents the rate at which energy is dissipated in the fluid. This study shows how reduced Hessian successive quadratic programming method, which avoid converging the flow equations at each iteration, can be tailored to these problems.