![]() We focus on the uniform Delaunay triangulation of planar regions and, in particular, on how one selects the positions of the vertices of the triangulation. Mesh generation in regions in Euclidean space is a central task in computational science, and especially for commonly used numerical methods for the solution of partial differential equations, e.g., finite element and finite volume methods. This example is used to elucidate both the potential benefits of this multiresolution method and the challenges ahead. Our numerical example is based on the nonlinear, shallow water equations spanning the entire surface of the sphere. In addition to defining, developing, and exhibiting SCVTs, we pair this mesh generation technique with a previously developed finite-volume method. Idealized examples are developed for ocean–ice shelf interaction and for regional atmospheric modeling. Real-world examples are developed for the Greenland ice sheet and the North Atlantic ocean. In each of the examples provided, this method results in high-quality meshes where the quality measures are guaranteed to improve as the number of nodes is increased. ![]() SCVTs allow for the generation of high quality Voronoi diagrams and Delaunay triangulations through the use of an intuitive, user-defined density function. Spherical centroidal Voronoi more » tessellations (SCVTs) offer one potential path toward the development of a robust, multiresolution climate system model components. These new demands will almost certainly result in the develop of multiresolution schemes that are able, at least regionally, to faithfully simulate these fine-scale processes. Each climate system component has its prototypical example of an unresolved process that may strongly influence the global climate system, ranging from eddy activity within ocean models, to ice streams within ice sheet models, to surface hydrological processes within land system models, to cloud processes within atmosphere models. = ,ĭuring the next decade and beyond, climate system models will be challenged to resolve scales and processes that are far beyond their current scope.
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