Spherical Centroidal Voronoi Tessellations Unstructured Meshes For Ocean Applications

Abstract

In the past and increasingly so towards the present, the modeling of our oceans is of great import. In order to facilitate this simulation, we wish to discretize the sphere in an optimal manner. That is to say, we wish to place the most grid points where we have the most information to capture. Here, we wish to support both local refinement and global refinement. To start, we use the theory of centroidal Voronoi tessellations on the sphere to give us a regular mesh. We supplement this with an approximation of the shoreline, which we use by both forcing generators to conform to it and regulating the density of generators based on their distance to it. In addition, away from the shoreline we vary the density based on some proxy information.