Data-driven modal decomposition methods as feature detection techniques for flow problems: a critical assessment

Abstract

Modal decomposition techniques are showing a fast growth in popularity for their good properties as data-driven tools. There are several modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are considered the most demanded methods, especially in the field of fluid dynamics. Following their magnificent performance on various applications in several fields, numerous extensions of these techniques have been developed. In this work we present an ambitious review comparing eight different modal decomposition techniques, including most established methods: POD, DMD and Fast Fourier Trasform (FFT), extensions of these classical methods: based on time embedding systems, Spectral POD (SPOD) and Higher Order DMD (HODMD), based on scales separation, multi-scale POD (mPOD), multi-resolution DMD (mrDMD), and based on the properties of the resolvent operator, the data-driven Resolvent Analysis (RA). The performance of all these techniques will be evaluated on three different testcases: the laminar wake around cylinder, a turbulent jet flow, and the three dimensional wake around cylinder in transient regime. First, we show a comparison between the performance of the eight modal decomposition techniques when the datasets are shortened. Next, all the results obtained will be explained in details, showing both the conveniences and inconveniences of all the methods under investigation depending on the type of application and the final goal (reconstruction or identification of the flow physics). In this contribution we aim on giving a -- as fair as possible -- comparison of all the techniques investigated. To the authors knowledge, this is the first time a review paper gathering all this techniques have been produced, clarifying to the community what is the best technique to use for each application.

References in corpus (6)

• Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data
• Frequency-time analysis, low-rank reconstruction and denoising of turbulent flows using SPOD
• From bypass transition to flow control and data-driven turbulence modeling: An input-output viewpoint
• SPOD and resolvent analysis of near-wall coherent structures in turbulent pipe flows
• Data-driven resolvent analysis
• Multiscale Proper Orthogonal Decomposition (mPOD) of TR-PIV data-- a Case Study on Stationary and Transient Cylinder Wake Flows

Cited by in corpus (2)

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