Modal Analysis of a Flow Past a Cylinder

Abstract

As the computational fluid mechanics community is advancing rapidly, the need to assimilate and compress the high-fidelity data is increasing simultaneously. Modal decomposition techniques like proper orthogonal decomposition and dynamic mode decomposition are widely used to capture important features (modes) of the flow field to facilitate reduced-order modeling. The frequency-domain equivalent of POD known as spectral proper orthogonal decomposition (SPOD) is currently emerging as a competitive alternative to these techniques. The present work analyzes the efficacy of SPOD compared to POD and DMD in obtaining effective latent space representations that enable accurate low-rank flow field reconstructions of unsteady flows. Suitability and shortcomings of the methods are highlighted for a canonical case of unsteady flow across a stationary cylinder at a Reynolds number of 100, based on the error metrics for low-rank reconstructions. It was observed that first two SPOD modes alone have constituted more than 90% of the energy in the flow. With just four SPOD modes, the flow field was reconstructed with less than 1% error, while it took six modes of POD and DMD to achieve the same accuracy.