Spherical shallow‐water wave simulation by a cubed‐sphere finite‐difference solver

Brachet, Matthieu; Croisille, Jean‐Pierre

doi:10.1002/qj.3946

Cited by 5 publications

(4 citation statements)

References 29 publications

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“…We expect that most numerical methods would perform well on these tests. This was the case for our experiments on both uniform and locally refined grids and was also noticed in Brachet and Croisille (2021) for a cubed-sphere based model.…”

Section: Matsuno Baroclinic Wavesupporting

confidence: 82%

Topography based local spherical Voronoi grid refinement on classical and moist shallow-water finite volume models

Santos¹,

Peixoto²

2021

Preprint

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Abstract. Locally refined grids for global atmospheric models are attractive since they are expected to provide an alternative to solve local phenomena without the requirement of a global high-resolution uniform grid, whose computational cost may be prohibitive. The Spherical Centroidal Voronoi Tesselations (SCVT), as used in the atmospheric Model for Prediction Across Scales (MPAS), allows a flexible way to build and work with local refinement. Alongside, the Andes Range plays a key role in the South American weather, but it is hard to capture its fine structure dynamics in global models. This paper describes how to generate SCVT grids that are locally refined in South America and that also capture the sharp topography of the Andes Range by defining a density function based on topography and smoothing techniques. We investigate the use of the mimetic finite volume scheme employed in the MPAS dynamical core on this grid considering the non-linear classic and moist shallow-water equations on the sphere. We show that the local refinement, even with very smooth transitions from different resolutions, generates spurious numerical inertia-gravity waves that may even numerically de-stabilize the model. In the moist shallow-water model, where physical processes such as precipitation and cloud formation are included, our results show that the local refinement may generate spurious rain that is not observed in uniform resolution SCVT grids. Fortunately, the spurious waves originate from small-scale grid-related numerical errors and therefore can be mitigated using small amounts of numerical diffusion. We show that, in some cases, the clouds are better represented in a variable resolution grid when compared to a respective uniform resolution grid with the same number of cells, while in other cases, grid effects can deteriorate the cloud and rain representation.

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Section: Matsuno Baroclinic Wavesupporting

confidence: 82%

Topography based local spherical Voronoi grid refinement on classical and moist shallow-water finite volume models

Santos¹,

Peixoto²

2021

Preprint

View full text Add to dashboard Cite

show abstract

Section: Matsuno Baroclinic Wavesupporting

confidence: 82%

Topography-based local spherical Voronoi grid refinement on classical and moist shallow-water finite-volume models

Santos

Peixoto

2021

Geosci. Model Dev.

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Abstract. Locally refined grids for global atmospheric models are attractive since they are expected to provide an alternative to solve local phenomena without the requirement of a global high-resolution uniform grid, whose computational cost may be prohibitive. Spherical centroidal Voronoi tessellation (SCVT), as used in the atmospheric Model for Prediction Across Scales (MPAS), allows a flexible way to build and work with local refinement. In addition, the Andes Range plays a key role in the South American weather, but it is hard to capture its fine-structure dynamics in global models. This paper describes how to generate SCVT grids that are locally refined in South America and that also capture the sharp topography of the Andes Range by defining a density function based on topography and smoothing techniques. We investigate the use of the mimetic finite-volume scheme employed in the MPAS dynamical core on this grid considering the nonlinear classic and moist shallow-water equations on the sphere. We show that the local refinement, even with very smooth transitions from different resolutions, generates spurious numerical inertia–gravity waves that may even numerically destabilize the model. In the moist shallow-water model, wherein physical processes such as precipitation and cloud formation are included, our results show that the local refinement may generate spurious rain that is not observed in uniform-resolution SCVT grids. Fortunately, the spurious waves originate from small-scale grid-related numerical errors and can therefore be mitigated using fourth-order hyperdiffusion. We exploit a grid geometry-based hyperdiffusion that is able to stabilize spurious waves and has very little impact on the total energy conservation. We show that, in some cases, the clouds are better represented in a variable-resolution grid when compared to a respective uniform-resolution grid with the same number of cells, while in other cases, grid effects can affect the cloud and rain representation.

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“…It arises in a variety of contexts in physics and chemistry: quantum physics, cristallography, gravimetry, astrophysics, kinetic theory (Boltzmann collision kernel approximations, neutron transport), to quote some of them. Our interest in this question stemed from numerical experiments with a Cubed Sphere nite dierence (FD) solver for the spherical shallow water equations, [8]. Important mean quantities must be accurately preserved with time, one of them beeing the mean potential vorticity.…”

Section: Discussionmentioning

confidence: 99%

Quadrature and symmetry on the Cubed Sphere

Bellet

Brachet

Croisille

2022

Journal of Computational and Applied Mathematics

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In the companion paper [6], a spherical harmonics subspace associated to the Cubed Sphere has been introduced. This subspace is further analyzed here. In particular, it permits to dene a new Cubed Sphere based quadrature. This quadrature inherits the rotationally invariant properties of the spherical harmonics subspace. Contrary to Gauss quadratures, where the set of nodes and weights is solution of a nonlinear system, only the weights are unknown here. Despite this conceptual simplicity, the new quadrature displays an accuracy comparable to optimal quadratures, such as the Lebedev rules.

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Spherical shallow‐water wave simulation by a cubed‐sphere finite‐difference solver

Cited by 5 publications

References 29 publications

Topography based local spherical Voronoi grid refinement on classical and moist shallow-water finite volume models

Topography based local spherical Voronoi grid refinement on classical and moist shallow-water finite volume models

Topography-based local spherical Voronoi grid refinement on classical and moist shallow-water finite-volume models

Quadrature and symmetry on the Cubed Sphere

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