Fast and high-order solutions to the spherical shallow water equations Original Research Article

Fast methods for computing the spatial derivatives of functions on the sphere are studied for use in explicit time-stepping approximations to the spherical shallow water equations. Filtering must be used to stabilize these methods, and attention is directed to Fourier and spherical harmonic filtering. Selected model problem results and filter timings are presented. Preliminary results indicate that spectral results can be achieved in approximately one-third the time of the spectral transform method.