Spatial Filtering for Reduced Order Modeling

TL;DR

This paper investigates spatial filtering in reduced order models, focusing on the Leray ROM and introducing a new ROM differential filter to improve flow simulation accuracy for flow past a cylinder.

Contribution

It introduces a novel ROM differential filter and evaluates its performance within the Leray ROM framework for flow simulation.

Findings

The new ROM differential filter improves flow simulation accuracy.

Spatial filtering effectively reduces energy aliasing in ROMs.

The methods are tested on flow past a circular cylinder at Re=760.

Abstract

Spatial filtering has been central in the development of large eddy simulation reduced order models (LES-ROMs) and regularized reduced order models (Reg-ROMs), In this paper, we perform a numerical investigation of spatial filtering. To this end, we consider one of the simplest Reg-ROMs, the Leray ROM (L-ROM), which uses ROM spatial filtering to smooth the flow variables and decreases the amount of energy aliased to the lower index ROM basis functions. We also propose a new form of ROM differential filter and use it as a spatial filter for the L-ROM. We investigate the performance of this new form of ROM differential filter in the numerical simulation of a flow past a circular cylinder at a Reynolds number $Re=760$.