Recursive Dynamic Mode Decomposition for the flow around two square cylinders in tandem configuration

A recent approach in modelling coherent structures in fluid flows, called Recursive Dynamic Mode Decomposition, is presented on the example of the flow around two square cylinders, where interactions between the wakes occur. The distance between cylinders varies from one to five side lengths of the square, leading to different behaviour of the wake flow. The proposed method is based on the recursive repeating of a three-step procedure: computation of the DMD mode basis, selection of the mode minimizing the defined residual error, and, finally, purging this mode from the flow (the snapshots). RDMD combines the advantages of Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). Low residual error, characteristic of POD, and purer frequency content observed in DMD, make this method especially applicable in unsupervised machine learning-based applications, including machine learning control (MLC) of the flows with few dominant frequencies (Brunton and Noack, 2015).

Automated summary

This article presents a modeling approach called Recursive Dynamic Mode Decomposition (RDMD) for studying coherent structures in fluid flows. The method effectively handles interactions between wakes and combines the advantages of Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). It is especially applicable in unsupervised machine learning applications, including machine learning control.