The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows

TL;DR

This paper compares two reduced order modeling strategies for incompressible Navier-Stokes equations across laminar and turbulent flows, introducing a new POD-Galerkin approach with eddy viscosity interpolation for turbulent regimes.

Contribution

It introduces a novel POD-Galerkin reduced order method incorporating eddy viscosity interpolation for turbulent flows, extending reduced order modeling to higher Reynolds numbers.

Findings

Effective reduced order models for laminar flows using stabilized finite element methods.

A new POD-Galerkin approach with eddy viscosity interpolation for turbulent flows.

Successful application to benchmark test cases across flow regimes.

Abstract

We present two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a stabilized finite element method during the offline stage followed by a Galerkin projection on reduced basis spaces generated by a greedy algorithm. The second methodology is based on a full order finite volume discretization. The latter methodology will be used for flows with moderate to high Reynolds number characterized by turbulent patterns. For the treatment of the mentioned turbulent flows at the reduced order level, a new POD-Galerkin approach is proposed. The new approach takes into consideration the contribution of the eddy viscosity also during the online stage and is based on the use of interpolation. The two methodologies are tested on classic benchmark test cases.