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

TL;DR

This paper introduces a Frontal-Delaunay refinement algorithm for generating high-quality, non-uniform unstructured grids on ellipsoidal geometries, suitable for atmospheric and ocean modeling, with improved element quality and efficiency.

Contribution

It presents a novel Frontal-Delaunay refinement technique for constructing high-quality unstructured ellipsoidal Delaunay triangulations and dual Voronoi-based polygonal grids for geophysical applications.

Findings

Produces near-optimal element quality grids

Generates smoothly graded non-uniform grids

Imposes low computational expense

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 near-optimal 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.