Numerical Solution of Optimal Control Problems Governed by
the Compressible Navier-Stokes Equations
S. Scott Collis
Department of Mechanical Engineering and Materials Science
Kaveh Ghayour
Department of Computational and Applied Mathematics and
Department of Mechanical Engineering and Materials Science
Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
Michael Ulbrich
Stefan Ulbrich
Zentrum Mathematik
Technische Universität München, Germany
Optimal Control of Complex Structures,
K.-H. Hoffmann and I. Lasiecka,
G. Leugering, J. Sprekels, F. Tröltzsch (eds.),
Birkhäuser Verlag,
International Series of Numerical Mathematics, Vol. 139,
2001, pages 43-55.
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.
See also
S. S. Collis, K. Ghayour, M. Heinkenschloss, M. Ulbrich,
and S. Ulbrich,
Optimal Control of Unsteady Compressible Viscous Flows.