A radial basis function method for the shallow water equations on a sphere

AMS Citation:
Flyer, N., and G. B. Wright, 2009: A radial basis function method for the shallow water equations on a sphere. Proceedings of the Royal Society. Series A, Mathematical Physical & Engineering Sciences, 465, 1949-1976, doi:10.1098/rspa.2009.0033.
Date:2009-06-08
Resource Type:article
Title:A radial basis function method for the shallow water equations on a sphere
Abstract: The paper derives the first known numerical shallow water model on the sphere using radial basis function (RBF) spatial discretization, a novel numerical methodology that does not require any grid or mesh. In order to perform a study with regard to its spatial and temporal errors, two nonlinear test cases with known analytical solutions are considered. The first is a global steady-state flow with a compactly supported velocity field, while the second is an unsteady flow where features in the flow must be kept intact without dispersion. This behaviour is achieved by introducing forcing terms in the shallow water equations. Error and time stability studies are performed, both as the number of nodes are uniformly increased and the shape parameter of the RBF is varied, especially in the flat basis function limit. Results show that the RBF method is spectral, giving exceptionally high accuracy for low number of basis functions while being able to take unusually large time steps. In order to put it in the context of other commonly used global spectral methods on a sphere, comparisons are given with respect to spherical harmonics, double Fourier series and spectral element methods.
Subject(s):Radial basis functions, Hyperbolic partial differential equations, Spherical geometry
Peer Review:Refereed
Copyright Information:An edited version of this paper was published by the Royal Society. Copyright 2009 the Royal Society.
OpenSky citable URL: ark:/85065/d7dn4680
Publisher's Version: 10.1098/rspa.2009.0033
Author(s):
  • Natasha Flyer - NCAR/UCAR
  • Grady Wright
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