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

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 $Re=100$.