Adaptive Atmospheric Modeling: Key Techniques in Grid by Jörn Behrens

By Jörn Behrens

This is an outline of the advance of adaptive innovations for atmospheric modeling. Written in a tutorial kind, it capabilities as a place to begin for readers drawn to adaptive modeling, in atmospheric sciences and past. assurance contains paradigms of adaptive suggestions, corresponding to mistakes estimation and edition standards. Mesh iteration tools are awarded for triangular/tetrahedral and quadrilateral/hexahedral meshes, with a unique part on preliminary meshes for the sphere.

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Additional info for Adaptive Atmospheric Modeling: Key Techniques in Grid Generation, Data Structures, and Numerical Operations with Applications (Lecture Notes in Computational Science and Engineering)

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5 Spherical Geometries [1,1,1] 41 [2,2,2] [0,0,1] [0,1,0] [0,0,0] [1,1,1] [1,0,0] [0,0,0] Fig. 18. 5 Spherical Geometries In order to find discrete representations of the sphere, we have to start with an initial triangulation T . In most cases, the sphere is triangulated by a 2D triangulation, which is extended to fully 3D geometries by layers of identical 2D grids. Triangular Initial Triangulations In this subsection we will introduce three different possibilities to triangulate a polygonal approximation to the sphere.

A 4deg × 4deg Lat-Lon grid is depicted in fig. 22. One possibility to circumvent the small mesh size near the poles is the Reduced Lat-Lon grid, an example of which is also depicted in fig. 22. Here the mesh size is doubled (several times) in the high latitudes, yielding an almost uniform mesh size on the whole sphere. Note that the pole singularity is not removed by this remedy. A semi-Lagrangian solution technique for the shallow water equations on a reduced grid can be found in [259]. A combination of spherical grid and spherically projected unit square grid at the poles, a so called capped sphere has been proposed by Lanser et al.

21. 4636) Note that the icosahedron is the dual to the dodecahedron, a polyhedron with 12 pentagonal faces. Therefore a triangulation of the dodecahedron results in the same grids as a triangulation of the icosahedron. An application using the icosahedral grid to derive a spherical geodesic grid is given in [339]. Finally, another possibility to define the initial triangulation of a sphere is to use the truncated icosahedron (better known as buckyball or simply soccer ball). The truncated icosahedron consists of 12 pentagons and 20 hexagons.

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