Polynomial identification of POD based low-order dynamical system

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Abstract
Low-order modelling based on POD approach has proved to be an efficient tool to analyze turbulent flows as well as to build control systems. In this paper, a novel method to identify low-order dynamical system (LODS) is proposed. This approach relies on the fact that all the POD-Galerkin LODS based on Navier–Stokes equations can be written in polynomial form. One proposes here to estimate the polynomial coefficients arising in such a formalism by the following. The projection coefficients of the flow field onto its POD basis and their time derivatives being known, a statistical approach involving correlations between these quantities, are used to provide an estimate of the coefficients of the dynamical system. The identification method is described and tested in the case of the analytical Lorenz system. Finally, the LODS identification is performed in the case of experimental data of a supersonic jet-mixing layer interaction. Dynamical systems based on flow visualizations are derived and lead to relevant short-time and long-term predictions.