Nonintrusive Stabilization of Reduced Order Models for Uncertainty Quantification of Time-Dependent Convection-Dominated Flows

TL;DR

This paper introduces a nonintrusive, filter-based stabilization technique for reduced order models to improve uncertainty quantification in convection-dominated fluid flows, combining high-order filtering with stochastic collocation methods.

Contribution

A novel high-order differential filter and evolve-filter-relax algorithm are developed for nonintrusive stabilization of ROMs in UQ of Navier-Stokes equations.

Findings

Effective attenuation of numerical oscillations in ROMs.

Successful integration of the framework with legacy solvers.

Accurate UQ results for flow past a cylinder with random viscosity.

Abstract

In this paper, we propose a nonintrusive filter-based stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the time-dependent Navier-Stokes equations in convection-dominated regimes. We propose a novel high-order ROM differential filter and use it in conjunction with an evolve-filter-relax algorithm to attenuate the numerical oscillations of standard ROMs. We also examine how stochastic collocation methods (SCMs) can be combined with the evolve-filter-relax algorithm for efficient UQ of fluid flows. We emphasize that the new stabilized SCM-ROM framework is nonintrusive and can be easily used in conjunction with legacy flow solvers. We test the new framework in the numerical simulation of a two-dimensional flow past a circular cylinder with a random viscosity that yields a random Reynolds number with mean $Re=100$.