Higher Order Dynamic Mode Decomposition to Model Reacting Flows

Abstract

This work presents a new application of higher order dynamic mode decomposition (HODMD) for the analysis of reactive flows. Due to the high complexity of the data analysed, consisting of more than 80 variables (i.e., temperature and chemically reacting species) a new extension of HODMD has been developed combining the multi-dimensional HODMD algorithm with classical preprocessing techniques generally used in machine learning analyses, such as principal component analysis (PCA). This new methodology has proved to be suitable to identify the main patterns driving the main dynamics of the flow, as well as to develop reduced order models grounded in physical principles. The new algorithm was tested by means of a database obtained from a Computational Fluid Dynamics simulation of an axy-symmetric time varying non-premixed co-flow nitrogen-diluted methane flame, carried out by means of a detailed kinetic mechanism. Different dynamics were identified, and they were associated to the different variables of the reactive flow analysed. Also, this algorithm has been coupled with an additional feature selection step carried out via PCA and varimax rotation. The results that were obtained by coupling PCA with varimax rotation show the outstanding capabilities of this novel methodology to compress original databases as function of the different preprocessing techniques that are used.