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Numerical Solution of Optimal Control Problems Governed by the Compressible Navier-Stokes Equations

S. Scott Collis+ Pfeil, Kaveh Gayour+*, Matthias Heinkenschloss* Pfeil, Michael Ulbrich**, and Stefan Ulbrich** Pfeil

+Department of Mechanical Engineering and Materials Science Rice University, Houston, TX 77005-1892, USA

*Department of Computational and Applied Mathematics Rice University, Houston, TX 77005-1892, USA

**Lehrstuhl für Angewandte Mathematik und Mathematische Statistik

Zentrum Mathematik

Technische Universität München

Technical Report

November 2000

In: Optimal Control of Complex Structures

K.-H. Hoffmann, I. Lasiecka, G. Leugering, J. Sprekels, and F. Tröltzsch (eds.)

Birkhäuser Verlag, 2001.

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Theoretical and practical issues arising in optimal boundary control of the unsteady two-dimensional compressible Navier-Stokes equations are discussed. Assuming a sufficiently smooth state, formal adjoint and gradient equations are derived. For a vortex rebound model problem wall normal suction and blowing is used to minimize cost functionals of interest, here the kinetic energy at the final time.