A reduced order variational multiscale approach for turbulent flows

• Published in: Advances in computational mathematics Vol. 45; no. 5-6; pp. 2349 - 2368
• Main Authors: Stabile, Giovanni, Ballarin, Francesco, Zuccarino, Giacomo, Rozza, Gianluigi
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2019; Springer Nature B.V
• Subjects: Computational fluid dynamics; Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Computer simulation; Galerkin method; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Model reduction of parametrized Systems; Multiscale analysis; Reduced order models; Stabilization; Visualization; Variational multiscale; 65N12; Reduced order methods; 76F65; 76D05; High Reynolds number flows; 65N30; Navier-Stokes equations
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-019-09712-x

The purpose of this work is to present different reduced order model strategies starting from full order simulations stabilized using a residual-based variational multiscale (VMS) approach. The focus is on flows with moderately high Reynolds numbers. The reduced order models (ROMs) presented in this manuscript are based on a POD-Galerkin approach. Two different reduced order models are presented, which differ on the stabilization used during the Galerkin projection. In the first case, the VMS stabilization method is used at both the full order and the reduced order levels. In the second case, the VMS stabilization is used only at the full order level, while the projection of the standard Navier-Stokes equations is performed instead at the reduced order level. The former method is denoted as consistent ROM , while the latter is named non-consistent ROM , in order to underline the different choices made at the two levels. Particular attention is also devoted to the role of inf-sup stabilization by means of supremizers in ROMs based on a VMS formulation. Finally, the developed methods are tested on a numerical benchmark.