System Identification For Enhanced Flow Description From Multi-Pulse PIV

We propose a novel approach to obtain a time-resolved description from non-time-resolved PIV measurements. The method needs in input velocity and acceleration fields from ( at least) 3-pulse PIV data, without time r esolution. A sparse identification of nonlinear dynamics (based on the SINDy technique) is carried out to estimate the time history of coordinates in a low-dimensional space from Proper Orthogonal Decomposition (POD). The output is a reduced-order model of the dynamics which can be integrated to obtain time-resolved velocity fields using t he s napshots as i nitial c onditions. The t ime-resolved e volution of t he pressure fields is th en derived from the momentum equation. The time history of the velocity and pressure fields is obtained through a weighted Backward-Forward Integration (BFI) of the identified s ystem. Time super-sampling can be achieved by integration between consecutive non-time-resolved realizations. In alternative, simple one-directional time integration can be used for short-time prediction starting from individual snapshots. The algorithm is validated using a synthetic test case from 2D Direct Numerical Simulation of the wake of a fluidic pinball at a Reynolds number Re equal to 130, and PIV measurements of the wake of a NACA 0018 wing profile with Re = 4 800. We show that the method is able to reconstruct the flow dynamics for horizons of several convective times, provided that the basis for the data reduction is sufficiently c ompact. Our results suggest that manifold learning and data assimilation can be combined to obtain an enhanced flow description.