Research Article

Optimal control of unsteady compressible viscous flows

  1. S. Scott Collis1,*,
  2. Kaveh Ghayour2,
  3. Matthias Heinkenschloss3,
  4. Michael Ulbrich4,
  5. Stefan Ulbrich5

Article first published online: 21 NOV 2002

DOI: 10.1002/fld.420

Issue

International Journal for Numerical Methods in Fluids

International Journal for Numerical Methods in Fluids

Volume 40, Issue 11, pages 1401–1429, 20 December 2002

Additional Information

How to Cite

Scott Collis, S., Ghayour, K., Heinkenschloss, M., Ulbrich, M. and Ulbrich, S. (2002), Optimal control of unsteady compressible viscous flows. International Journal for Numerical Methods in Fluids, 40: 1401–1429. doi: 10.1002/fld.420

Author Information

  1. 1

    Department of Mechanical Engineering and Materials Science, Rice University, Houston, TX 77005-1892, U.S.A.

  2. 2

    Department of Computational and Applied Mathematics and Department of Mechanical Engineering and Materials Science, Rice University, Houston, TX 77005-1892, U.S.A.

  3. 3

    Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005-1892, U.S.A.

  4. 4

    Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, D-20146 Hamburg, Germany

  5. 5

    Lehrstuhl für Angewandte Mathematik und Mathematische Statistik, Zentrum Mathematik, Technische Universität München, D-80290 München, Germany

*Department of Mechanical Engineering and Materials Science, Rice University, Houston, TX 77005-1892, U.S.A.

Publication History

  1. Issue published online: 21 NOV 2002
  2. Article first published online: 21 NOV 2002
  3. Manuscript Revised: 22 JUL 2002
  4. Manuscript Received: 21 MAY 2002

Funded by

  • Texas ATP. Grant Number: 003604-001-1999
  • Los Alamos Computer Science Institute. Grant Number: 03891-99-23
  • DFG. Grant Numbers: UL157/3-1, UL158/2-1
  • CRPC. Grant Number: CCR-9120008
  • NSF SCREMS. Grant Number: 98-72009

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Keywords:

  • optimal flow control;
  • compressible Navier–Stokes equations;
  • gradient computation

Abstract

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two-dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter-rotating viscous vortices above an infinite wall which, due to the self-induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall-normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.

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