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- 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- 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.
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Michele Girfoglio 1; Annalisa Quaini 2; Gianluigi Rozza 1
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@article{CRMECA_2023__351_S1_457_0,
author = {Michele Girfoglio and Annalisa Quaini and Gianluigi Rozza},
title = {A linear filter regularization for {POD-based} reduced-order models of the quasi-geostrophic equations},
journal = {Comptes Rendus. M\'ecanique},
pages = {457--477},
publisher = {Acad\'emie des sciences, Paris},
volume = {351},
number = {S1},
year = {2023},
doi = {10.5802/crmeca.183},
language = {en},
}
TY - JOUR AU - Michele Girfoglio AU - Annalisa Quaini AU - Gianluigi Rozza TI - A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations JO - Comptes Rendus. Mécanique PY - 2023 SP - 457 EP - 477 VL - 351 IS - S1 PB - Académie des sciences, Paris DO - 10.5802/crmeca.183 LA - en ID - CRMECA_2023__351_S1_457_0 ER -
%0 Journal Article %A Michele Girfoglio %A Annalisa Quaini %A Gianluigi Rozza %T A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations %J Comptes Rendus. Mécanique %D 2023 %P 457-477 %V 351 %N S1 %I Académie des sciences, Paris %R 10.5802/crmeca.183 %G en %F CRMECA_2023__351_S1_457_0
Michele Girfoglio; Annalisa Quaini; Gianluigi Rozza. A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations. Comptes Rendus. Mécanique, The scientific legacy of Roland Glowinski, Volume 351 (2023) no. S1, pp. 457-477. doi : 10.5802/crmeca.183. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.183/
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