A dynamic mode decomposition technique for the analysis of non–uniformly sampled flow data

Abstract

A novel Dynamic Mode Decomposition (DMD) technique capable of handling non–uniformly sampled data is proposed. As it is usual in DMD analysis, a linear relationship between consecutive snapshots is made. The performance of the new method, which we term θ-DMD, is assessed on three different, increasingly complex datasets: a synthetic flow field, a ReD=60 flow around a cylinder cross section, and a Reτ=200 turbulent channel flow. For the three datasets considered, whenever the dataset is uniformly sampled, the θ-DMD method provides comparable results to the original DMD method. Additionally, the θ-DMD is still capable of recovering relevant flow features from non–uniformly sampled databases, whereas DMD cannot. The proposed tool opens the way to conduct DMD analyses for non–uniformly sampled data, and can be useful e.g., when confronted with experimental datasets with missing data, or when facing numerical datasets generated using adaptive time-integration schemes.