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

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