Rotational transport on a sphere: Local node refinement for radial basis functions

AMS Citation:
Flyer, N., and E. Lehto, 2010: Rotational transport on a sphere: Local node refinement for radial basis functions. Journal of Computational Physics, 229, 1954-1969, doi:10.1016/j.jcp.2009.11.016.
Date:2010-03-20
Resource Type:article
Title:Rotational transport on a sphere: Local node refinement for radial basis functions
Abstract: This paper develops an algorithm for radial basis function (RBF) local node refinement and implements it for vortex roll-up and transport on a sphere. A heuristic based on an electrostatic repulsion type principle is used to re-distribute the nodes, clustering in areas where higher resolution is needed. It is then important to have a scheme that varies the shape of the RBFs over the domain so as to counteract the effects of Runge phenomena where the nodes are sparse. The roll-up of two diametrically opposed moving vortices are studied. The performance differences between near-uniform and refined nodes are addressed in terms of convergence, time stability, and computational cost. RBF results are put into context by comparison with published results for methods such as finite volume and discontinuous Galerkin.
Subject(s):Radial basis functions, Local node refinement, Hyberbolic PDEs
Peer Review:Refereed
Copyright Information:NOTICE: This is the author's version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.
OpenSky citable URL: ark:/85065/d7w66nbw
Publisher's Version: 10.1016/j.jcp.2009.11.016
Author(s):
  • Natasha Flyer - NCAR/UCAR
  • Erik Lehto
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