Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey   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.

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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int