Data-driven variational multiscale reduced order models
Data-driven variational multiscale reduced order models
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DOI：
10.1016/j.cma.2020.113470
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发表时间：
2021-01-01
影响因子：
7.2
通讯作者：
Iliescu, Traian
中科院分区：
文献类型：
--
作者：
Mou, Changhong;Koc, Birgul;Iliescu, Traian
我们提出了一种新的数据驱动的降阶模型（ROM）框架，该框架以变分多尺度（VMS）方法的层次结构为中心，并利用数据以适度的计算成本提高ROM精度。VMS方法非常适合ROM基础的层次结构：在第一步中，我们使用ROM投影将尺度分为三类：(i)已解决的大尺度，（ii）已解决的小尺度和（iii）未解决的尺度。在第二步中，我们明确地确定VMS-ROM闭合术语，即表示三种类型尺度之间相互作用的术语。在第三步中，我们使用可用数据对VMS-ROM关闭项进行建模。因此，我们利用现有的数据来构建新的结构VMS- rom闭合模型，而不是VMS中用于标准数值离散化的现象学模型（例如，涡流粘度模型）。具体来说，我们构建的ROM运算符（向量、矩阵和张量）最接近用可用数据计算的真实ROM闭包项。我们在四个测试用例中对新的数据驱动VMS-ROM进行了数值模拟：(i)粘度系数nu = 10（-3）的1D Burgers方程；（ii）雷诺数Re = 100、Re = 500和Re = 1000时流过圆柱体的二维流动；（iii）雷诺数Re = 450、罗斯比数Ro = 0.0036时的准地转方程；（iv）雷诺数Re = 1000时后向阶跃的二维流动。数值结果表明，数据驱动的VMS-ROM的精度明显高于标准rom。(C) 2020 Elsevier B.V.版权所有
We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost. The VMS methodology is a natural fit for the hierarchical structure of the ROM basis: In the first step, we use the ROM projection to separate the scales into three categories: (i) resolved large scales, (ii) resolved small scales, and (iii) unresolved scales. In the second step, we explicitly identify the VMS-ROM closure terms, i.e., the terms representing the interactions among the three types of scales. In the third step, we use available data to model the VMS-ROM closure terms. Thus, instead of phenomenological models used in VMS for standard numerical discretizations (e.g., eddy viscosity models), we utilize available data to construct new structural VMS-ROM closure models. Specifically, we build ROM operators (vectors, matrices, and tensors) that are closest to the true ROM closure terms evaluated with the available data. We test the new data-driven VMS-ROM in the numerical simulation of four test cases: (i) the 1D Burgers equation with viscosity coefficient nu = 10(-3); (ii) a 2D flow past a circular cylinder at Reynolds numbers Re = 100, Re = 500, and Re = 1000; (iii) the quasi-geostrophic equations at Reynolds number Re = 450 and Rossby number Ro = 0.0036; and (iv) a 2D flow over a backward facing step at Reynolds number Re = 1000. The numerical results show that the data-driven VMS-ROM is significantly more accurate than standard ROMs. (C) 2020 Elsevier B.V. All rights reserved.