A Discontinuous Galerkin Global Shallow Water Model

By Ramachandran D. Nair, Stephen J. Thomas, R. Loft. Monthly Weather Review, 2005

194 citations recorded by the source corpus.

A discontinuous Galerkin shallow water model on the cubed sphere is developed, thereby extending the transport scheme developed by Nair et al. The continuous flux form nonlinear shallow water equations in curvilinear coordinates are employed. The spatial discretization employs a modal basis set consisting of Legendre polynomials. Fluxes along the element boundaries (internal interfaces) are approximated by a Lax–Friedrichs scheme. A third-order total variation diminishing Runge–Kutta scheme is applied for time integration, without any filter or limiter. Numerical results are reported for the standard shallow water test suite. The numerical solutions are very accurate, there are no spurious oscillations in test case 5, and the model conserves mass to machine precision. Although the scheme does not formally conserve global invariants such as total energy and potential enstrophy, conservation of these quantities is better preserved than in existing finite-volume models.

Subfields: Atmospheric Science, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/770c00a4526bd97a8873d3cebd8e2378cf3f2d5d

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Citations in the corpus

High-order h-adaptive discontinuous Galerkin methods for ocean modelling (2007, background): “Dynamic mesh adaptation strategies following those structures represent a great potential in the field of ocean modelling (e.g. Behrens 1998; Heinze and Hense 2002; Nair et al. 2005; Giraldo et al. 2002).”
Horizontal grids for global weather and climate prediction models: a review (2012, unknown): “a pentagonal-hexagonal A-grid), Tomita et al. (2002) initialised it with an analytic, balanced, solid-body, rotational flow, sampled at gridpoints.”
Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere (2023, methodology): “…(Hersbach et al., 2020), one of the best estimates of Earth’s historical weather and climate over the period 1950-present, and to the rotating Spherical Shallow Water Equations (SWE), which are commonly used to model geophysical fluid dynamical phenomena (Nair et al., 2005; Bonev et al., 2018).”
A Survey of High Order Schemes for the Shallow Water Equations (2014, background): “Several advantages of the DGmethod, including its high order accuracy, high parallel efficiency, flexibility for hp-adaptivity and arbitrary geometry and meshes, make it suited for the SWEs, see [16, 19, 23, 38, 51].”
NCAR Release of CAM‐SE in CESM2.0: A Reformulation of the Spectral Element Dynamical Core in Dry‐Mass Vertical Coordinates With Comprehensive Treatment of Condensates and Energy (2018, methodology): “…expressed in tensor form using conventional notations as the covariant (u1, u2) and contravariant (u1, u2) vectors using the 2 × 2 transformation matrix D associated with the gnomonic mapping such that DT D = Gij (see Nair et al. (2005) for the details): [ u v ] = D [ u1 u2 ] = D−T [ u1 u2 ] .”