基于pod的准地转方程降阶模型的线性滤波正则化

IF 1.2 4区 化学 Q3 CHEMISTRY, MULTIDISCIPLINARY
Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza
{"title":"基于pod的准地转方程降阶模型的线性滤波正则化","authors":"Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza","doi":"10.5802/crmeca.183","DOIUrl":null,"url":null,"abstract":"We propose a regularization for reduced-order models (ROMs) of the quasi-geostrophic equations (QGE) to increase accuracy when the proper orthogonal decomposition (POD) modes retained to construct the reduced basis are insufficient to describe the system dynamics. Our regularization is based on the so-called BV-α model, which modifies the nonlinear term in the QGE and adds a linear differential filter for the vorticity. To show the effectiveness of the BV-α model for ROM closure, we compare the results computed by a POD-Galerkin ROM with and without regularization for the classical double-gyre wind forcing benchmark. Our numerical results show that the solution computed by the regularized ROM is more accurate, even when the retained POD modes account for a small percentage of the eigenvalue energy. Additionally, we show that, although computationally more expensive than the ROM with no regularization, the regularized ROM is still a competitive alternative to full-order simulations of the QGE.","PeriodicalId":10566,"journal":{"name":"Comptes Rendus. Chimie","volume":"85 1","pages":"0"},"PeriodicalIF":1.2000,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations\",\"authors\":\"Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza\",\"doi\":\"10.5802/crmeca.183\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a regularization for reduced-order models (ROMs) of the quasi-geostrophic equations (QGE) to increase accuracy when the proper orthogonal decomposition (POD) modes retained to construct the reduced basis are insufficient to describe the system dynamics. Our regularization is based on the so-called BV-α model, which modifies the nonlinear term in the QGE and adds a linear differential filter for the vorticity. To show the effectiveness of the BV-α model for ROM closure, we compare the results computed by a POD-Galerkin ROM with and without regularization for the classical double-gyre wind forcing benchmark. Our numerical results show that the solution computed by the regularized ROM is more accurate, even when the retained POD modes account for a small percentage of the eigenvalue energy. Additionally, we show that, although computationally more expensive than the ROM with no regularization, the regularized ROM is still a competitive alternative to full-order simulations of the QGE.\",\"PeriodicalId\":10566,\"journal\":{\"name\":\"Comptes Rendus. Chimie\",\"volume\":\"85 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-03-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus. Chimie\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/crmeca.183\",\"RegionNum\":4,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus. Chimie","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/crmeca.183","RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 3

摘要

本文提出了准地转方程(QGE)的降阶模型(ROMs)的正则化方法,以提高用于构造降阶基的正交分解(POD)模式不足以描述系统动力学时的精度。我们的正则化基于所谓的BV-α模型,该模型修改了QGE中的非线性项,并为涡度增加了线性微分滤波器。为了证明BV-α模型对ROM关闭的有效性,我们比较了POD-Galerkin ROM对经典双环流风强迫基准的正则化和非正则化计算结果。数值结果表明,即使保留的POD模式占特征值能量的百分比很小,正则化ROM计算的解也更准确。此外,我们表明,虽然计算成本比没有正则化的ROM高,但正则化ROM仍然是QGE全阶模拟的一个有竞争力的替代方案。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations
We propose a regularization for reduced-order models (ROMs) of the quasi-geostrophic equations (QGE) to increase accuracy when the proper orthogonal decomposition (POD) modes retained to construct the reduced basis are insufficient to describe the system dynamics. Our regularization is based on the so-called BV-α model, which modifies the nonlinear term in the QGE and adds a linear differential filter for the vorticity. To show the effectiveness of the BV-α model for ROM closure, we compare the results computed by a POD-Galerkin ROM with and without regularization for the classical double-gyre wind forcing benchmark. Our numerical results show that the solution computed by the regularized ROM is more accurate, even when the retained POD modes account for a small percentage of the eigenvalue energy. Additionally, we show that, although computationally more expensive than the ROM with no regularization, the regularized ROM is still a competitive alternative to full-order simulations of the QGE.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Comptes Rendus. Chimie
Comptes Rendus. Chimie 化学-化学综合
CiteScore
2.10
自引率
25.00%
发文量
89
审稿时长
3 months
期刊介绍: The Comptes Rendus - Chimie are a free-of-charge, open access and peer-reviewed electronic scientific journal publishing original research articles. It is one of seven journals published by the Académie des sciences. Its objective is to enable researchers to quickly share their work with the international scientific community. The Comptes Rendus - Chimie also publish journal articles, thematic issues and articles reflecting the history of the Académie des sciences and its current scientific activity.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信