Nonlinear Reduced Order Modeling using Domain Decomposition

Abstract

View Video Presentation: https://doi.org/10.2514/6.2022-1250.vid As designers become increasingly reliant upon expensive, high-fidelity numerical modeling and simulation, Reduced Order Modeling (ROM) has emerged as a compelling method of predicting high-dimensional discretized field outputs in a compact and efficient manner. This study presents a parametric, non-intrusive ROM which uses Domain Decomposition (DD) and is capable of employing multiple dimension reduction techniques within different spatial sub-domains of the field. To enforce smoothness of solutions across sub-domains, points at domain interfaces are masked and the Gappy Proper Orthogonal Decomposition (Gappy-POD) method is used to reconstruct the global solution. The methodology is assessed on three test cases, including two-dimensional turbulent flow around the RAE2822. Results show that nonlinear ROMs predict fields more accurately in the vicinity of discontinuous features compared to their linear counterparts, which are more accurate in regions that are far from these discontinuities. Furthermore, application of DD using nonlinear ROMs only in the vicinity of a discontinuity resulted in predictive error reduction near the shockwave and significant improvement in total error compared to existing approaches that employ a single global model. Finally, Gappy-POD was shown to provide smooth field predictions with linear DDROMs, though its performance deteriorated with nonlinear methods.