Sangam: A Confluence of Knowledge Streams

Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey

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dc.contributor Mathematics
dc.creator Mou, Changhong
dc.creator Wang, Zhu
dc.creator Wells, David R.
dc.creator Xie, Xuping
dc.creator Iliescu, Traian
dc.date 2021-01-08T15:50:29Z
dc.date 2021-01-08T15:50:29Z
dc.date 2020-12-31
dc.date 2021-01-08T14:48:13Z
dc.date.accessioned 2023-03-01T18:53:30Z
dc.date.available 2023-03-01T18:53:30Z
dc.identifier Mou, C.; Wang, Z.; Wells, D.R.; Xie, X.; Iliescu, T. Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey. Fluids 2020, 6, 16.
dc.identifier http://hdl.handle.net/10919/101803
dc.identifier https://doi.org/10.3390/fluids6010016
dc.identifier.uri http://localhost:8080/xmlui/handle/CUHPOERS/281732
dc.description Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, finite difference, finite volume, or spectral methods). Thus, ROMs have been used to accelerate numerical simulations of many query problems, e.g., uncertainty quantification, control, and shape optimization. Projection-based ROMs have been particularly successful in the numerical simulation of fluid flows. In this brief survey, we summarize some recent ROM developments for the quasi-geostrophic equations (QGE) (also known as the barotropic vorticity equations), which are a simplified model for geophysical flows in which rotation plays a central role, such as wind-driven ocean circulation in mid-latitude ocean basins. Since the QGE represent a practical compromise between efficient numerical simulations of ocean flows and accurate representations of large scale ocean dynamics, these equations have often been used in the testing of new numerical methods for ocean flows. ROMs have also been tested on the QGE for various settings in order to understand their potential in efficient numerical simulations of ocean flows. In this paper, we survey the ROMs developed for the QGE in order to understand their potential in efficient numerical simulations of more complex ocean flows: We explain how classical numerical methods for the QGE are used to generate the ROM basis functions, we outline the main steps in the construction of projection-based ROMs (with a particular focus on the under-resolved regime, when the closure problem needs to be addressed), we illustrate the ROMs in the numerical simulation of the QGE for various settings, and we present several potential future research avenues in the ROM exploration of the QGE and more complex models of geophysical flows.
dc.description Published version
dc.format application/pdf
dc.format application/pdf
dc.language en
dc.publisher MDPI
dc.rights Creative Commons Attribution 4.0 International
dc.rights http://creativecommons.org/licenses/by/4.0/
dc.subject reduced order models
dc.subject quasi-geostrophic equations
dc.subject closure models
dc.title Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey
dc.title Fluids
dc.type Article - Refereed
dc.type Text


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