On the optimization of flow control actuators

The objective of this work is to construct reduced-order models based on POD ("Proper Orthogonal Decomposition") that are able to accurately reproduce the spatio-temporal dynamics of separated flows. The growing interest concerning these models comes from their potential use in the resolution of large scale constrained optimization problems, in the context of flow control. The general approach consists in substituting the high-fidelity model of the Navier-Stokes equations by an approximate model, cheaper to compute and capturing the essential features of the original dynamics. POD, which is the optimal decomposition in terms of energy, allows to approximate the flow dynamics in a subspace spanned by a few number of modes. Different calibration methods are developed here in order to improve the accuracy of the reduced-order models, and thus make this approach suitable for flow control issues. Essentially, the idea of the calibration methods is to determine in the equations of the POD reduced-order models auxiliary parameters that are computed by resolving appropriate constrained minimization problems.