Convergence of POD Modes for Cylinder Wake Flow

Abstract

Proper orthogonal decomposition (POD) is a popular technique for both flow analysis and model order reduction. However, its applicability is strongly dependent on the amount of input data. In the present contribution, we investigate the convergence of numerical POD modes for the canonical case of turbulent flow in the wake behind a circular cylinder. In particular, the cylinder placed at a crossflow at Reynolds number of 4815 was simulated using detached eddy simulation (DES) with sufficient mesh resolution to achieve a large eddy simulation (LES) and direct numerical simulation (DNS) blend in the region of interest located directly behind the examined cylinder. The convergence of POD modes with respect to (i) the number of temporal snapshots used, (ii) the enforcement of the assumed symmetries, and (iii) spatial resolution of the CFD results was examined. Only the first eleven modes can be assumed converged when using standard POD and 12000 snapshots sampled at 2 kHz. However, the results may be significantly improved by enforcing symmetries in the data, which enables to converge even the fifteenth mode with a significantly lower number of snapshots. Finally, simple norm-based techniques did not proved to be a sufficient tool for POD toposes comparison. Therefore the quantitative evaluation of the modes convergence remains an open question.