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

Title: 通过空间滤波连接对流主导流动的大涡模拟和降阶建模：综述与展望

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. Show Chinese abstract

Abstract: 降阶模型（ROMs）在许多学科中已经取得了很大的成功，能够降低传统数值方法的计算成本。然而，对于对流主导（例如，湍流）流动，标准的ROMs通常会产生不准确的结果，通常受到虚假振荡的影响。因此，ROMs通常配备数值稳定化或闭合模型，以考虑被丢弃模态的影响。关于ROM闭合和稳定化的文献数量庞大且增长迅速。在本文中，我们关注一种特定类型的ROM闭合和稳定化，这些方法受到大涡模拟（LES）的启发。这些ROMs，我们称之为LES-ROMs，非常容易实现，非常高效且准确。经过仔细调整的LES-ROMs可以在许多应用中准确捕捉对流主导流动中的平均物理量。LES-ROMs是通过利用空间滤波构建的，即用于构建经典LES模型的相同原理。这确保了LES-ROMs与生成训练数据的方法之间的一致性。它还“连接”了两个不同的研究领域（LES和ROMs），这两个领域此前一直互不关联。本文是对LES-ROMs的综述。它首先描述了一种称为 evolve-filter-relax（EFR）的通用LES策略，该策略已被成功用作全阶方法。然后，我们展示了如何利用EFR策略以及一般的空间滤波来构建LES-ROMs。介绍了LES-ROMs的几个应用。最后，我们得出结论，并概述了LES-ROM开发中的几个研究方向和开放问题。虽然我们并不声称这篇综述是全面的，但我们确实希望它能作为这一令人兴奋的研究领域的简短而友好的介绍，该领域在对流主导流动的实际数值模拟中具有很大的潜力。