Consistency of the full and reduced order models for evolve‐filter‐relax regularization of convection‐dominated, marginally‐resolved flows. (25th March 2022)

• Record Type: Journal Article
• Authors: Strazzullo, Maria; Girfoglio, Michele; Ballarin, Francesco; Iliescu, Traian; Rozza, Gianluigi
• Is Part Of: International journal for numerical methods in engineering. Volume 123:Number 14(2022)
• Page Start: 3148
• Page End: 3178
• Publication Date: 2022-03-25
• Subjects: evolve‐filter‐relax stabilization -- marginally‐resolved convection‐dominated flows -- Navier–Stokes equations -- proper orthogonal decomposition -- reduced order modeling; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6942
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: Numerical stabilization is often used to eliminate (alleviate) the spurious oscillations generally produced by full order models (FOMs) in under‐resolved or marginally‐resolved simulations of convection‐dominated flows. In this article, we investigate the role of numerical stabilization in reduced order models (ROMs) of marginally‐resolved, convection‐dominated incompressible flows. Specifically, we investigate the FOM–ROM consistency, that is, whether the numerical stabilization is beneficial both at the FOM and the ROM level. As a numerical stabilization strategy, we focus on the evolve‐filter‐relax (EFR) regularization algorithm, which centers around spatial filtering. To investigate the FOM‐ROM consistency, we consider two ROM strategies: (i) the EFR‐noEFR, in which the EFR stabilization is used at the FOM level, but not at the ROM level; and (ii) the EFR‐EFR, in which the EFR stabilization is used both at the FOM and at the ROM level. We compare the EFR‐noEFR with the EFR‐EFR in the numerical simulation of a 2D incompressible flow past a circular cylinder in the convection‐dominated, marginally‐resolved regime. We also perform model reduction with respect to both time and Reynolds number. Our numerical investigation shows that the EFR‐EFR is more accurate than the EFR‐noEFR, which suggests that FOM‐ROM consistency is beneficial in convection‐dominated, marginally‐resolved flows.