Computation and Analysis of Flow Control and Optimization Problems
Abstract
In the first part of the talk, after a brief historical introduction, we
consider algorithms for solving flow control and optimization problems and
the results of the application of these algorithms in a number of settings.
The former include sensitivity and adjoint based methods while the latter
include temperature and flow matching examples, optimal shape design in
flows with shock waves, and delaying transition to turbulence in boundary
layer flows. Among the types of controls or design parameters we consider
are fluid injection or suction, temperature or heat flux at boundaries, and
the shape of part of the boundary of the flow domain. At the end of the
talk, we consider the analysis of boundary velocity control of the
Navier-Stokes system for time-dependent, incompressible, viscous flows. In
particular, for a drag minimization problem, we show that optimal solutions
exist, that the Lagrange multiplier rule may be used to enforce
constraints, and derive an optimality system of partial differential
equations from which optimal controls and states may be determined. Along
the way, we also prove some new results concerning the time-dependent
Navier Stokes system with inhomogeneous boundary conditions.
