Todd D. Ringler, Theoretical Division, Los Alamos National Laboratory
Doug Jacobsen, Department of Scientific Computing, Florida State University
Over the last decade the climate modeling community has worked toward the construction of component models that are situated on quasi-uniform tessellations of the sphere, such as the cubed-sphere and icosahedral meshes. With completion of that goal in sight, we press forward and explore the notion of utilizing multiple resolutions within a single mesh that tessellates the sphere. In this approach we employ Spherical Centroidal Voronoi Tessellations (SCVTs) that allow for the construction of high-quality, variable-resolution meshes. We pair the SCVTs with a recently developed finite-volume solver that maintains all of the relevant conservation properties even when the underlying mesh is highly distorted.
Our approach is to generate high-quality SCVTs that result in two dominate resolutions, where one resolution (the fine scale) covers the region of interest and the other resolution (the coarse scale) covers the rest of the sphere. The two dominate scales are separated by a mesh transition zone that, like the fine and coarse scales, is easily altered through the user-specified mesh-density function. We apply our finite-volume solver along with these variable resolution SCVTs to the standard suite of shallow-water test cases in order to highlight the strengths and weakens of this multi-resolution approach.
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