2010
DOI: 10.1016/j.jcp.2009.12.007
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Abstract: A numerical scheme applicable to arbitrarily structured C-grids is presented for the nonlinear shallow-water equations. By discretizing the vector invariant form of the momentum equation, the relationship between the nonlinear Coriolis force and the potential vorticity flux can be used to guarantee that mass, velocity and potential vorticity evolve in a consistent and compatible manner. Underpinning the consistency and compatibility of the discrete system is the construction of an auxiliary thickness equation … Show more

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Cited by 270 publications
(399 citation statements)
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“…Centroidal Voronoi tessellations are particularly well-suited for the generation of smoothly varying meshes, thus providing a possible alternative to traditional nesting approaches. With the recent discovery of a class of finite-volume methods that are directly applicable to variable resolution meshes ( (Thuburn et al, 2009;Ringler et al, 2010)), it appears that the creation of variable resolution, global climate system models is now possible.…”
Section: Discussionmentioning
confidence: 99%
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“…Centroidal Voronoi tessellations are particularly well-suited for the generation of smoothly varying meshes, thus providing a possible alternative to traditional nesting approaches. With the recent discovery of a class of finite-volume methods that are directly applicable to variable resolution meshes ( (Thuburn et al, 2009;Ringler et al, 2010)), it appears that the creation of variable resolution, global climate system models is now possible.…”
Section: Discussionmentioning
confidence: 99%
“…C-grid staggering has shown promising results, particularly when applied to variable resolution meshes. See Check: Ringler Dyncore Chapter for a broad discussion of C-grid staggerings and see (Thuburn et al, 2009;Ringler et al, 2010) for an in-depth discussion of C-grid staggering applied to the nonlinear shallow-water equations.…”
Section: Example Numerical Methodsmentioning
confidence: 99%
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“…Control volumes for mass, tracers and entropy/potential temperature are the hexagonal cells of the Voronoi mesh to avoid the fast numerical modes of the triangular C-grid. The horizontal discretization is that of Ringler et al (2010), whose discrete quasi-Hamiltonian structure is identified. The prognostic variables are arranged vertically on a Lorenz grid with all thermodynamical variables collocated with mass.…”
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confidence: 99%