{"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}
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.
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.