2019/01/15 by Luigi C. Berselli, Traian Iliescu, Berselli, Luigi C. +5
Physics and Astronomy · Engineering · #Model Reduction and Neural Networks #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis
paper · pdf · doi:10.48550/arxiv.1901.04903
We perform a theoretical and numerical investigation of the time-average of\nenergy exchange among modes of Reduced Order Models (ROMs) of fluid flows. We\nare interested in the statistical equilibrium problem, and especially in the\npossible forward and backward average transfer of energy among ROM basis\nfunctions (modes). We consider two types of ROM modes: eigenfunctions of the\nStokes operator and Proper Orthogonal Decomposition (POD) modes. We prove\nanalytical results for both types of ROM modes and we highlight the differences\nbetween them. We also investigate numerically whether the time-average energy\nexchange between POD modes is positive. To this end, we utilize the\none-dimensional Burgers equation as a simplified mathematical model, which is\ncommonly used in ROM tests. The main conclusion of our numerical study is that,\nfor long enough time intervals, the time-average energy exchange from low index\nPOD modes to high index POD modes is positive, as predicted by our theoretical\nresults.\n