A reduced order variational multiscale approach for turbulent flows

TL;DR

This paper introduces a reduced order modeling framework for turbulent flows using a variational multiscale approach combined with POD-Galerkin methods, comparing consistent and non-consistent stabilization strategies.

Contribution

It presents two novel reduced order models with different stabilization techniques within the VMS framework for turbulent flows.

Findings

Both models effectively capture turbulent flow dynamics.

The consistent ROM shows improved stability over the non-consistent version.

Inf-sup stabilization via supremizers enhances ROM accuracy.

Abstract

The purpose of this work is to present a reduced order modeling framework for parametrized turbulent flows with moderately high Reynolds numbers within the variational multiscale (VMS) method. The Reduced Order Models (ROMs) presented in this manuscript are based on a POD-Galerkin approach with a VMS stabilization technique. 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 level. 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.