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

Fast methods for computing the spatial derivatives of functions on the sphe re are studied for use in explicit time-stepping approximations to the sphe rical shallow water equations. Filtering must be used to stabilize these me thods, and attention is directed to Fourier and spherical harmonic filterin g. Selected model problem results and filter timings are presented. Prelimi nary results indicate that spectral results can be achieved in approximatel y one-third the time of the spectral transform method, (C) 2000 IMACS. Publ ished by Elsevier Science B.V. All rights reserved.