Natasha Flyer
Dept. of Applied Mathematics
University of Colorado
Boulder, Colorado, USA
Since the early 1990s, radial basis functions (RBFs) have been applied to solve simple elliptical and mixed parabolic partial differential equations (PDEs). Not until 2003 has applications to spherical geometries been considered, with implementation of RBFs only to low algebraic accuracy. In this current presentation, we will solve for the first time ever purely hyperbolic PDEs on a sphere using RBFs to spectral accuracy. The two test cases that will be considered are linear advection of a height field over the surface of the sphere and deformational flow that models the spin up of two diametrically opposed vortices. Performance of the presented RBF methodology will be evaluated through considerations on accuracy, time stability, and comparisons with other commonly featured methods.