Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 465, Issue 2106, Pages 1949-1976Publisher
ROYAL SOC
DOI: 10.1098/rspa.2009.0033
Keywords
radial basis functions; hyperbolic partial differential equations; spherical geometry
Categories
Funding
- National Science Foundation
- NSF [ATM-0620100, ATM-0801309]
- Div Atmospheric & Geospace Sciences
- Directorate For Geosciences [0801309] Funding Source: National Science Foundation
Ask authors/readers for more resources
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. at 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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available