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.

翻译：降阶模型（ROMs）在降低传统数值方法计算成本方面取得了显著成功。然而，对于对流主导（例如湍流）流动，标准ROM通常会产生不准确的结果，且常受伪振荡影响。因此，ROM通常需配备数值稳定化方法或闭合模型以考虑被截断模态的影响。关于ROM闭合与稳定化的文献数量庞大且增长迅速。本文聚焦于一类受大涡模拟（LES）启发的特定ROM闭合与稳定化方法。这类我们称之为LES-ROM的模型具有极易实现、高效且精确的特点。经精心调参的LES-ROM能够在众多应用场景中准确捕捉挑战性对流主导流动的平均物理量。LES-ROM的构建基于空间滤波原理——这与经典LES模型的构建原理相同。这确保了LES-ROM与用于训练其的数据生成方法之间的建模一致性，同时“连接”了迄今仍相互独立的两大研究领域（LES与ROM）。本文是对LES-ROM的综述。首先描述一种称为演化-滤波-松弛（EFR）的通用LES策略，该策略已成功用作全阶方法。随后阐述如何利用EFR策略及广义空间滤波构建LES-ROM，并展示LES-ROM的若干应用案例。最后总结结论，并展望LES-ROM发展的若干研究方向与开放问题。尽管本文不宣称综述内容面面俱到，但我们期望它能作为对这一充满潜力的研究领域的简要友好导引，为实际对流主导流动的数值模拟提供重要参考。