Comptes Rendus
A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations
Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 457-477.

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.

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Published online:
DOI: 10.5802/crmeca.183
Keywords: Quasi-geostrophic equations, Proper orthogonal decomposition, Reduced-order model, Galerkin projection, Filter regularization

Michele Girfoglio 1; Annalisa Quaini 2; Gianluigi Rozza 1

1 mathLab, Mathematics Area, SISSA, via Bonomea 265, I-34136 Trieste, Italy
2 Department of Mathematics, University of Houston, Houston TX 77204, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     journal = {Comptes Rendus. M\'ecanique},
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Michele Girfoglio; Annalisa Quaini; Gianluigi Rozza. A linear filter regularization for POD-based reduced-order models of the quasi-geostrophic equations. Comptes Rendus. Mécanique, 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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