POD-based Reduced-Order Modeling in Fluid Flows using System Identification Strategy

The representation of flow field via reduced order models (ROM) has proven to be successful in reducing the degree of freedom of the system. ROM can be developed in two ways: (a) system identification techniques and b) Galerkin projection of Proper orthogonal decomposition (POD) modes onto the Governing equations such as Navier-Stokes equations. In this study, we investigate a canonical problem of incompressible flow past a circular cylinder. We first compute the POD modes and then determine the corresponding temporal coefficients. Some of these coefficients are used as training data for system identification techniques. We employ two regressive methods as a system identification strategy for predicting the temporal coefficients of ROM. On the other hand, we also develop a ROM through Galerkin projection technique and compare it with the system identification techniques. Based on this comparison, we have discussed the accuracy, advantages, and limitations of these methods in ROM.