Frequency-domain proper orthogonal decomposition for efficient reconstruction of unsteady flows

Proper orthogonal decomposition (POD) is a widely used data-driven, reduced-order method for feature extraction and field reconstruction of unsteady flows. The number of modes required in the POD varies greatly with the flow characteristics, and a high number of modes is a significant challenge to effective multiscale flow analysis. The first part of this study shows that the number of modes required for flow field reconstruction increases almost linearly with the energy proportion of the stochastic fluctuation, making it costly to accurately reconstruct the stochastic fluctuation in unsteady flows. To address this issue, the second part of this study proposes a frequency domain proper orthogonal decomposition (FDPOD) method, which reduces the number of modes required for accurate reconstruction while preserving key spectral characteristics of the unsteady flow. Three case studies, i.e., cylinder flow, jet flow, and fan flow, are employed to illustrate the advantage of the developed FDPOD method, which provides a more accurate and efficient tool for turbulence analysis, especially for multiscale flows dominated by stochastic fluctuations.