Optimal Control of Unsteady Viscous Flows

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

International Journal for Numerical Methods in Fluids,
Vol. 40 (2002), No. 11, pp. 1401-1429.

Abstract

This paper is concerned with 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, adjoint computations, as well as the impact of the inner product in the control space on the gradient computation 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. Different objectives and different control regularizations are studied.