Numerical Analysis of the Leray Reduced Order Model
For researchers in computational fluid dynamics, this work offers rigorous error bounds for a regularized ROM that reduces spurious oscillations in convection-dominated flows.
The paper provides numerical analysis of the Leray reduced order model (ROM), proving error estimates for the ROM differential filter and the Leray ROM, and validating them numerically on 2D Navier-Stokes equations with an analytic solution.
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.