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Multi-resolution unstructured grid-generation for geophysical applications on the sphere

Engwirda, Darren

24th International Meshing Roundtable, Elsevier Ltd., pp.Research Note, October 12-14 2015

IMR
PROCEEDINGS

24th International Meshing Roundtable
Austin, TX
October 12-14,2014

Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 54-918, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 USA
Email: engwirda@mit.edu

Abstract
An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinement technique, a method for the construction of high-quality unstructured ellipsoidal Delaunay triangulations is introduced. A dual polygonal grid, derived from the associated Voronoi diagram, is also optionally generated as a by-product. Compared to existing techniques, it is shown that the Frontal-Delaunay approach typically produces grids with nearoptimal element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform ellipsoidal grids appropriate for large-scale geophysical applications. The use of user-defined mesh-sizing functions to generate smoothly graded, non-uniform grids is discussed.

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