An adaptive solver for the spherical shallow water equations
2009 - L. Gavete, B. Alonso, M.L. Gavete, F. Ureña, J.J. Benito
Mathematics and Computers in Simulation, 79, 3466-3477 (2009)
Ureña Prieto, Francisco.
The shallow water equations (SWE), which describe the flow of a thin layer of fluid in two dimensions have been used by the atmospheric modelling community as a vehicle for testing promising numerical methods for solving atmospheric and oceanic problems. The SWE are important for the study of the dynamics of large-scale flows, as well for the development of new numerical schemes that are applied to more complex models. In this paper we present a finite difference p-adaptive method based on high order finite differences that is applied using an error indicator for solving the SWE on the sphere. A standard test set is used to evaluate the accuracy of the new method. The results obtained are compared with the pseudo-spectral method.