Approximating a branch of solutions to the Navier--Stokes equations by reduced-order modeling

TL;DR

This paper develops an advanced reduced-order modeling technique using low-rank tensor decomposition to accurately simulate viscous flows governed by the Navier-Stokes equations across a wide range of Reynolds numbers, with improved accuracy and insights.

Contribution

It introduces a non-interpolatory LRTD-ROM method that enhances accuracy and extends predictive capabilities for viscous flow solutions over a broad Reynolds number range.

Findings

Accurately predicts flow statistics for Reynolds numbers 25 to 400.

Outperforms previous ROMs in accuracy over wider Reynolds number ranges.

Provides new insights into parametric solution properties.

Abstract

This paper extends a low-rank tensor decomposition (LRTD) reduced order model (ROM) methodology to simulate viscous flows and in particular to predict a smooth branch of solutions for the incompressible Navier-Stokes equations. Additionally, it enhances the LRTD-ROM methodology by introducing a non-interpolatory variant, which demonstrates improved accuracy compared to the interpolatory method utilized in previous LRTD-ROM studies. After presenting both the interpolatory and non-interpolatory LRTD-ROM, we demonstrate that with snapshots from a few different viscosities, the proposed method is able to accurately predict flow statistics in the Reynolds number range $[25,400]$. This is a significantly wider and higher range than state of the art (and similar size) ROMs built for use on varying Reynolds number have been successful on. The paper also discusses how LRTD may offer new insights into the properties of parametric solutions.