Bridging Large Eddy Simulation and Reduced Order Modeling of Convection-Dominated Flows through Spatial Filtering: Review and Perspectives

TL;DR

This review explores LES-inspired reduced order models (LES-ROMs) for convection-dominated flows, highlighting their construction via spatial filtering, advantages, applications, and future research directions.

Contribution

It provides a comprehensive overview of LES-ROMs, connecting LES and ROMs, and discusses the evolve-filter-relax strategy for constructing efficient, accurate models.

Findings

LES-ROMs effectively capture physical quantities in turbulent flows.

Spatial filtering ensures modeling consistency between LES and ROMs.

LES-ROMs are easy to implement and computationally efficient.

Abstract

Reduced order models (ROMs) have achieved a lot of success in reducing the computational cost of traditional numerical methods across many disciplines. For convection-dominated (e.g., turbulent) flows, however, standard ROMs generally yield inaccurate results, usually affected by spurious oscillations. Thus, ROMs are usually equipped with numerical stabilization or closure models to account for the effect of the discarded modes. The literature on ROM closures and stabilizations is large and growing fast. In this paper, we focus on one particular type of ROM closures and stabilizations that are inspired by Large Eddy Simulation (LES). These ROMs, which we call LES-ROMs, are extremely easy to implement, very efficient, and accurate. Carefully tuned LES-ROMs can accurately capture the average physical quantities of interest in challenging convection-dominated flows in many applications. LES-ROM are constructed by leveraging spatial filtering, i.e., the same principle used to build classical LES models. This ensures a modeling consistency between LES-ROMs and the approaches that generated the data used to train them. It also ``bridges'' two distinct research fields (LES and ROMs), disconnected until now. This paper is a review of LES-ROMs. It starts with a description of a versatile LES strategy called evolve-filter-relax (EFR) that has been successfully used as a full order method. We then show how the EFR strategy, and spatial filtering in general, can be leveraged to construct LES-ROMs. Several applications of LES-ROMs are presented. Finally, we draw conclusions and outline several research directions and open questions in the LES-ROM development. While we do not claim this review to be comprehensive, we certainly hope it serves as a brief and friendly introduction to this exciting research area, which has a lot of potential in practical numerical simulation of convection-dominated flows.