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https://doi.org/10.5194/egusphere-2023-1715
https://doi.org/10.5194/egusphere-2023-1715
27 Sep 2023
 | 27 Sep 2023

MQGeometry-1.0: a multi-layer quasi-geostrophic solver on non-rectangular geometries

Louis Thiry, Long Li, Guillaume Roullet, and Etienne Mémin

Abstract. This paper presents MQGeometry, a multi-layer quasi-geostrophic (QG) equations solver for non-rectangul ar geometries. We advect the potential voriticity (PV) with finite volumes to ensure global PV conservation thanks to a staggered discretization of the PV and stream-function (SF). Thanks to this staggering, the PV is defined inside the domain, removing the need for defining the PV on the domain's boundary. We compute PV fluxes with upwind-biased interpolations whose implicit dissipation replaces the usual explicit (hyper-)viscous dissipation. The presented discretization does not require the tuning of any additional parameter, e.g. additional eddy viscosity. We solve the QG elliptic equation with a fast discrete sine transform spectral solver on rectangular geometry. We extend this fast solver to non-rectangular geometries using the capacitance matrix method. We validate our solver on a vortex-shear instability test case in a circular domain, a vortex-wall interaction test-case, and on an idealized wind-driven double-gyre configuration in a octogonal domain at a eddy-permitting resolution. We release a concise, efficient, and auto-differentiable PyTorch implementation of our method to facilitate future developments upon this new discretization, e.g. machine learning parameterization or data-assimilation techniques.

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Journal article(s) based on this preprint

28 Feb 2024
MQGeometry-1.0: a multi-layer quasi-geostrophic solver on non-rectangular geometries
Louis Thiry, Long Li, Guillaume Roullet, and Etienne Mémin
Geosci. Model Dev., 17, 1749–1764, https://doi.org/10.5194/gmd-17-1749-2024,https://doi.org/10.5194/gmd-17-1749-2024, 2024
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We present a new way of solving the quasi-geostrophic (QG) equations, a simple set of equations...
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