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

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 (by branch we refer to the continuation of the solution over a range of viscosities). 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 the statistics of a 2D flow passing a cylinder 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.