A global eigenvalue reassignment method for the stabilization of nonlinear reduced‐order models. (10th February 2021)

• Record Type: Journal Article
• Authors: Rezaian, Elnaz; Wei, Mingjun
• Is Part Of: International journal for numerical methods in engineering. Volume 122:Number 10(2021)
• Page Start: 2393
• Page End: 2416
• Publication Date: 2021-02-10
• Subjects: eigenvalue reassignment -- nonlinear systems -- POD‐Galerkin projection -- reduced‐order modeling -- stabilization; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6625
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: The systematic and physics‐infused construction of a projection‐based reduced‐order model (ROM) shows the capability to replicate the original high‐dimensional system's dynamical evolution but with a fractional computational cost. However, certain nonlinear features and high‐frequency contributions may be lost throughout the aggressive order reduction. Thus, ROMs in a broad category of fluid dynamics applications require stabilization and closure methods to compensate for the key contributions missed through the model order reduction. A new stabilization method for nonlinear ROMs is proposed in this study that learns a linear control law to drive the nonlinear ROM toward maximum agreement with the full‐order model, where a total power constraint guarantees the stability of the nonlinear ROM. This new method achieves both stability and accuracy for nonlinear proper orthogonal decomposition‐Galerkin ROMs in two chosen applications with strong shock‐wake interactions and unsteady oscillations, which trigger strong instabilities in the original ROMs before stabilization. A multistage layout is designed to further enhance the proposed stabilization method for more efficient and robust stabilization of nonlinear ROMs with a large number of unstable modes.