Regularized Reduced Order Modeling for Convection Dominated Flows

Jorge Reyes, Ping-Hsaun Tsai, Traian Iliescu

Abstract

This talk focuses on the development and motivations behind regularized reduced order models (ROMs) for turbulent flow. However, despite advances in high-performance computing}, when it comes to decision-making applications that require multiple forward simulations are needed, such as parameter study, design optimization, optimal control, uncertainty quantification, and inverse problems, the computational cost becomes prohibitive. ROMs have been shown to provide an efficient alternative. In the case of under-resolved flows, which is generally the case for high Reynolds numbers i.e. convection dominated flows, standard ROM accuracy tends to suffer. Regularization, which is based on spatial filtering, increases the ROM stability and accuracy at a negligible overhead. In this talk, I will outline several regularized ROMs that have been proven effective in the numerical simulation of under-resolved turbulent flows.