Applications of Higher Order Dynamic Mode Decomposition

Abstract

We present a method, higher order dynamic mode decomposition (HODMD) that is suitable to analyze flow structures of complex flows. These types of flows are found in nature or in several industrial applications, such as aerospace engineering, food processing or even physiological fluids. For this reason, studying and understanding complex flow behavior is a research topic of high interest. HODMD has been successfully applied to study several types of complex flows that cover from non-linear dynamical systems, to complex fluid dynamic problems. The method combines singular value decomposition (SVD) with DMD and Takens' delay embedding theorem to approximate flow dynamics.

In this seminar, we will present the good performance of HODMD applied to study noisy experimental data (transitional or thermal flow), and its extrapolation properties, which make this method a suitable tool that can be used to reduce the computational cost in numerical simulations. Finally, we will briefly introduce the spatio-temporal HODMD analysis, to calculate flow structures, defined as traveling waves. Some examples such as the analysis of a rotating spherical shell with thermal convection or the analysis of the wake of a wind turbine, will be presented at the time of the conference.