Konstantin Afanasiev, Michael Hinze:

Adaptive control of a wake flow using proper orthogonal decomposition

We present an effective quasi-optimal control method for the instationary Navier-Stokes equations. It in an adaptive manner utilizes the snapshot form of the proper orthogonal decomposition to construct a low dimensional approximation of the Navier-Stokes equations which then is used as subsidiary condition in the underlying optimization problem. The numerical solution of the reduced control problem is used as control for the full equations and to compute new snapshots. The set of the new snapshots then is added to the set of the snapshots already available, the low dimensional approximation of the Navier-Stokes equations is re-computed and the reduced optimization is restarted. This process is iterated until convergence is achieved. As numerical example we present tracking-type control of the periodic flow around a cylinder. The numerical results of the quasi-optimal approach are compared to that of the optimal approach.

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