On the construction of the Voronoi mesh on a sphere

Augenbaum, J. M.; Peskin, Charles S.

doi:10.1016/0021-9991(85)90140-8

Cited by 81 publications

(35 citation statements)

References 8 publications

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“…The number of total grid points for resolution M is N = 10 M 2 + 2. The hexagonal mesh is constructed as the Voronoi diagram of the triangular mesh (Augenbaum and Peskin, 1985). This ensures that primal and dual edges are orthogonal, a requirement of the numerical scheme.…”

Section: Outlook For Dynamicomentioning

confidence: 99%

DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility

Dubos¹,

Dubey

Tort³

et al. 2015

Geosci. Model Dev.

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Abstract. The design of the icosahedral dynamical core DY-NAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations in a Lagrangian vertical coordinate, and the primitive equations in a hybrid mass-based vertical coordinate. The common Hamiltonian structure of these sets of equations is exploited to formulate energy-conserving spatial discretizations in a unified way.The horizontal mesh is a quasi-uniform icosahedral C-grid obtained by subdivision of a regular icosahedron. 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. The vertical discretization is obtained from the three-dimensional Hamiltonian formulation. Tracers are transported using a second-order finite-volume scheme with slope limiting for positivity. Explicit Runge-Kutta time integration is used for dynamics, and forward-in-time integration with horizontal/vertical splitting is used for tracers. Most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately.Representative three-dimensional test cases are run and analyzed, showing correctness of the model. The design permits to consider several extensions in the near future, from higher-order transport to more general dynamics, especially deep-atmosphere and non-hydrostatic equations.

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Section: Outlook For Dynamicomentioning

confidence: 99%

DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility

Dubos¹,

Dubey

Tort³

et al. 2015

Geosci. Model Dev.

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“…al. (Augenbaum, 1984;Augenbaum et al, 1985). Randall (Randall, 1994) would later show that the collocation of variables in the vorticity-divergence system, termed the Z-grid, leads to a simulation of geostrophic adjustment that is better than any of the other staggerings based on primitive variables.…”

Section: In 2009mentioning

confidence: 99%

Voronoi Tessellations and Their Application to Climate and Global Modeling

Ringler

Gunzburger

2011

Lecture Notes in Computational Science and Engineering

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We review the use of Voronoi tessellations for grid generation, especially on the whole sphere or in regions on the sphere. Voronoi tessellations and the corresponding Delaunay tessellations in regions and surfaces on Euclidean space are defined and properties they possess that make them well-suited for grid generation purposes are discussed, as are algorithms for their construction. This is followed by a more detailed look at one very special type of Voronoi tessellation, the centroidal Voronoi tessellation (CVT). After defining them, discussing some of their properties, and presenting algorithms for their construction, we illustrate the use of CVTs for producing both quasi-uniform and variable resolution meshes in the plane and on the sphere. Finally, we briefly discuss the computational solution of model equations based on CVTs on the sphere.

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“…Here, a Voronoi cell is associated with each grid point [9]. Given a set of N grid points {P 1 , P 2 , .…”

Section: Figmentioning

confidence: 99%

Discrete Spherical Laplacian Operator

Funaki

2016

IEICE Trans. Inf. & Syst.

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SUMMARYLaplacian operator is a basic tool for image processing. For an image with regular pixels, the Laplacian operator can be represented as a stencil in which constant weights are arranged spatially to indicate which picture cells they apply to. However, in a discrete spherical image the image pixels are irregular; thus, a stencil with constant weights is not suitable. In this paper a spherical Laplacian operator is derived from Gauss's theorem; which is suitable to images with irregular pixels. The effectiveness of the proposed discrete spherical Laplacian operator is shown by the experimental results. key words: spherical camera model, discrete spherical image, Laplacian operator

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On the construction of the Voronoi mesh on a sphere

Cited by 81 publications

References 8 publications

DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility

DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility

Voronoi Tessellations and Their Application to Climate and Global Modeling

Discrete Spherical Laplacian Operator

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