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Technical Report

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


S. Scott Collis+, Kaveh Gayour+*, Matthias Heinkenschloss*,

Michael Ulbrich**, and Stefan Ulbrich**

+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

November 2000

Technical Report
Zentrum Mathematik
Technische Universität München

In: Optimal Control of Complex Structures
K.-H. Hoffmann, I. Lasiecka, G. Leugering, J. Sprekels, and F. Tröltzsch (eds.)
Birkhäuser Verlag, 2001.

as PDF file (504k).


Abstract

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.