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...
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Académie des sciences
2023-03-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.183/ |
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| author | Girfoglio, Michele Quaini, Annalisa Rozza, Gianluigi |
| author_facet | Girfoglio, Michele Quaini, Annalisa Rozza, Gianluigi |
| author_sort | Girfoglio, Michele |
| collection | DOAJ |
| description | 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-$\alpha $ 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-$\alpha $ 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. |
| format | Article |
| id | doaj-art-46e9e40a2bc54bf0b1a45de194d04e16 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-46e9e40a2bc54bf0b1a45de194d04e162025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-03-01351S145747710.5802/crmeca.18310.5802/crmeca.183A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equationsGirfoglio, Michele0https://orcid.org/0000-0003-1766-2265Quaini, Annalisa1https://orcid.org/0000-0001-9686-9058Rozza, Gianluigi2https://orcid.org/0000-0002-0810-8812mathLab, Mathematics Area, SISSA, via Bonomea 265, I-34136 Trieste, ItalyDepartment of Mathematics, University of Houston, Houston TX 77204, USAmathLab, Mathematics Area, SISSA, via Bonomea 265, I-34136 Trieste, ItalyWe 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-$\alpha $ 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-$\alpha $ 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.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.183/Quasi-geostrophic equationsProper orthogonal decompositionReduced-order modelGalerkin projectionFilter regularization |
| spellingShingle | Girfoglio, Michele Quaini, Annalisa Rozza, Gianluigi A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations Comptes Rendus. Mécanique Quasi-geostrophic equations Proper orthogonal decomposition Reduced-order model Galerkin projection Filter regularization |
| title | A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations |
| title_full | A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations |
| title_fullStr | A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations |
| title_full_unstemmed | A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations |
| title_short | A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations |
| title_sort | linear filter regularization for pod based reduced order models of the quasi geostrophic equations |
| topic | Quasi-geostrophic equations Proper orthogonal decomposition Reduced-order model Galerkin projection Filter regularization |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.183/ |
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