论文标题
减少订单模型关闭：简短教程
Reduced Order Model Closures: A Brief Tutorial
论文作者
论文摘要
在本文中，我们介绍了一个简短的教程，介绍了减少订单模型（ROM）关闭。首先，我们仔细地激发了在分辨不足的模拟中进行ROM封闭建模的需求。然后，我们通过将经典的Galerkin框架扩展到已解决和未解决的尺度的空间来逐步构建ROM闭合模型。最后，我们开发了数据驱动的变异多尺度闭合，然后在流体流量模拟中测试它。 我们关于ROM关闭的教程的结构是一系列问题和答案，针对第一年的研究生和高级本科生。我们的目标不是解释“如何”，而是“为什么”。也就是说，我们仔细解释了用于开发ROM封闭的原则，而无需关注特定方法。此外，我们尝试将技术细节保持在最低限度，并以广泛的方式描述一般思想，同时引用适当的参考文献以获取细节。
In this paper, we present a brief tutorial on reduced order model (ROM) closures. First, we carefully motivate the need for ROM closure modeling in under-resolved simulations. Then, we construct step by step the ROM closure model by extending the classical Galerkin framework to the spaces of resolved and unresolved scales. Finally, we develop the data-driven variational multiscale ROM closure and then we test it in fluid flow simulations. Our tutorial on ROM closures is structured as a sequence of questions and answers, and is aimed at first year graduate students and advanced undergraduate students. Our goal is not to explain the "how," but the "why." That is, we carefully explain the principles used to develop ROM closures, without focusing on particular approaches. Furthermore, we try to keep the technical details to a minimum and describe the general ideas in broad terms while citing appropriate references for details.
