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VORTEX METHODS AND VORTEX MODELS FOR FLOW CONTROL PROBLEMS

        Bartosz PROTAS
        Department of Mathematics and Statistics
        McMaster University,
        Hamilton, ON, Canada
        Email: bprotas@mcmaster.ca
        URL:   www.math.mcmaster.ca/~bprotas

In this presentation we will discuss two Lagrangian approaches
to the problem of flow control: a vortex method used as a tool
for solution of adjoint equations arising in flow optimization
problems, and a point vortex model used as an "ultimate reduced
order model" for feedback control design. Both these strategies
are derived using methods of Modern Control Theory and their 
precise mathematical characterization will be presented together 
with computational results. The two approaches represent two 
opposite extremes as regards complexity of the underlying models
and to fix attention in the talk we will focus on rotational 
control of laminar vortex shedding in the wake behind a circular 
cylinder. In the first strategy we seek to determine the optimal 
control for the full Navier-Stokes system by minimizing a cost 
functional which represents the drag. The cost functional 
gradient is determined using adjoint equations which are solved 
in the Lagrangian (vorticity) formulation. This control strategy 
leads to significant sustained drag reduction obtained with a 
very small control effort. The method, however, is very costly 
as regards the computational cost. In the second approach we 
use the F\"oppl system (1913) as a reduced order model for 
vortex shedding in the cylinder wake. This model will be 
characterized from the control-theoretic perspective. It will 
be shown that the cylinder wake can be stabilized using a 
Linear-Quadratic-Gaussian (LQG) feedback control design based 
on the F\"oppl model. The two approaches will be compared and 
perspectives will be outlined as regards design of intermediate 
approaches that could bridge vortex methods and vortex models
for flow control purposes.

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Professor Protas will also give a more specialized talk in the morning:

Department of Computer Science Numerical Analysis Seminar
10:10 AM Friday 12 November in Bahen Center (BA) Room 1210

"TOWARDS A MULTI-SCALE FRAMEWORK FOR COMPUTATIONAL
 FLOW CONTROL AND ESTIMATION"

http://www.math.toronto.edu/i-aim/public/Abstracts/protas.10am