Numerical analysis of the Leray reduced order model

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:328

Article

Xie, Xuping¹  Wells, David²  Wang, Zhu³  Iliescu, Traian¹ 

[1] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

[2] Rensselaer Polytech Inst, Dept Math Sci, Troy, NY 12180 USA

[3] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

关键词: Reduced order model;    Proper orthogonal decomposition;    Regularized model;    Leray model;    Spatial filter;   

DOI  :  10.1016/j.cam.2017.06.026

来源: Elsevier

【 摘 要 】

Standard ROMs generally yield spurious numerical oscillations in the simulation of convection-dominated flows. Regularized ROMs use explicit ROM spatial filtering to decrease these spurious numerical oscillations. The Leray ROM is a recently introduced regularized ROM that utilizes explicit ROM spatial filtering of the convective term in the Navier-Stokes equations. This paper presents the numerical analysis of the finite element discretization of the Leray ROM. Error estimates for the ROM differential filter, which is the explicit ROM spatial filter used in the Leray ROM, are proved. These ROM filtering error estimates are then used to prove error estimates for the Leray ROM. Finally, both the ROM filtering error estimates and the Leray ROM error estimates are numerically investigated in the simulation of the two-dimensional Navier Stokes equations with an analytic solution. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free