POD-spectral decomposition for fluid flow analysis and model reduction

Abstract

We propose an algorithm that combines proper orthogonal decomposition with a spectral method to analyze and extract reduced ordermodels of flows from time data series of velocity fields. The flows considered in this study are assumed to be driven by non-linear dynamical systems exhibiting a complex behavior within quasiperiodic orbits in the phase space. The technique is appropriate to achieve efficient reduced order models even in complex cases for which the flow description requires a discretization with a fine spatial and temporal resolution. The proposed analysis enables to decompose complex flow dynamics into modes oscillating at a single frequency. These modes are associated with different energy levels and spatial structures. The approach is illustrated using time-resolved PIV data of a cylinder wake flow with associated Reynolds number equal to 3,900.