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 wide range of applications and their various properties, especially as data-driven tools. There are many modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are the most widespread methods, especially in the field of fluid dynamics. Following their highly competent 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, i.e., POD, DMD, and Fast Fourier Transform; extensions of these classical methods: based either on time embedding systems, Spectral POD and Higher Order DMD, or based on scales separation, multi-scale POD (mPOD) and multi-resolution DMD (mrDMD); and also a method based on the properties of the resolvent operator, the data-driven Resolvent Analysis. The performance of all these techniques will be evaluated on four different test cases: the laminar wake around cylinder, a turbulent jet flow, the three-dimensional wake around a cylinder in transient regime, and a transient and turbulent wake around a cylinder. All these mentioned datasets are publicly available. 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 detail, 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 at 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 these techniques have been produced, clarifying to the community what is the best technique to use for each application.