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Large-Scale Optimization with Applications pp 247–270Cite as

Large-Scale SQP Methods for Optimization of Navier-Stokes Flows

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 93))

Abstract

We consider the problem of optimal control of fluids governed by the steady Navier-Stokes equations. 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. We show how reduced Hessian successive quadratic programming methods, which avoid converging the flow equations at each iteration, can be tailored to these problems. Both quasi-Newton and Newton variants are developed, and compared to the approach of eliminating the flow equations and variables, which is effectively the reduced gradient method. The examples demonstrate at least an order-of-magnitude reduction in time taken, allowing the optimal solution of realistic two-dimensional flow control problems in little time on a desktop workstation.

Supported in part by the Engineering Design Research Center, an Engineering Research Center of the National Science Foundation, under Grant No. EEC-8943164, and by Algor, Inc..

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Author information

Authors and Affiliations

  1. Computational Mechanics Laboratory, Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Omar Ghattas & Jai-Hyeong Bark

Authors
  1. Omar Ghattas
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  2. Jai-Hyeong Bark
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Editor information

Editors and Affiliations

  1. Chemical Engineering Department, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Lorenz T. Biegler

  2. Computer Science Department, Cornell University, Ithaca, NA, 14853-0001, USA

    Thomas F. Coleman

  3. Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, USA

    Andrew R. Conn

  4. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Fadil N. Santosa

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© 1997 Springer Science+Business Media New York

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Ghattas, O., Bark, JH. (1997). Large-Scale SQP Methods for Optimization of Navier-Stokes Flows. In: Biegler, L.T., Coleman, T.F., Conn, A.R., Santosa, F.N. (eds) Large-Scale Optimization with Applications. The IMA Volumes in Mathematics and its Applications, vol 93. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1960-6_11

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  • DOI: https://doi.org/10.1007/978-1-4612-1960-6_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7356-1

  • Online ISBN: 978-1-4612-1960-6

  • eBook Packages: Springer Book Archive

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