Regularized Reduced Order Models for a Stochastic Burgers Equation

TL;DR

This paper investigates the stability issues of reduced order models for a stochastic Burgers equation and demonstrates that the Leray regularization improves accuracy and robustness against noise-induced oscillations.

Contribution

The study introduces the use of Leray reduced order models to enhance numerical stability and accuracy in convection-dominated stochastic systems.

Findings

Leray reduced order model reduces spurious oscillations.

Leray model improves robustness to noise variations.

Standard models exhibit inaccuracies in convection-dominated regimes.

Abstract

In this paper, we study the numerical stability of reduced order models for convection-dominated stochastic systems in a relatively simple setting: a stochastic Burgers equation with linear multiplicative noise. Our preliminary results suggest that, in a convection-dominated regime, standard reduced order models yield inaccurate results in the form of spurious numerical oscillations. To alleviate these oscillations, we use the Leray reduced order model, which increases the numerical stability of the standard model by smoothing (regularizing) the convective term with an explicit spatial filter. The Leray reduced order model yields significantly better results than the standard reduced order model and is more robust with respect to changes in the strength of the noise.