Proper-Orthogonal-Decomposition–Based Emulation of Spatiotemporal Evolution of Turbulent Wakes

We present a nonintrusive surrogate model to emulate time-dependent flow problems. Our approach enhances spatial mode decomposition using proper orthogonal decomposition (POD) to spectral model decomposition via spectral POD (SPOD), along with mapping of the spectrum in each case onto a common spectral domain. This alignment enables the collapse of fundamental frequencies in different cases into a single frequency. To emulate a new flowfield, we apply the kriging method to predict the SPOD coefficients for the target case, followed by flowfield reconstruction using the inverse Fourier transform. In our examples of flow past circular and square cylinders, we demonstrate the limitations of emulation based on POD or SPOD without a common spectral domain, as they fail to predict the fundamental frequency accurately. However, our proposed approach employing SPOD in the rescaled spectral domain successfully predicts the velocity spectrum and achieves a good predictability for time-dependent lift and mean drag. Moreover, we underscore the necessity of unbiased training data for the method’s efficacy. This study proposes a robust, nonintrusive surrogate modeling strategy to capture time-dependent features of flow problems, which is crucial for design purposes where time dependency between parameters is significant.