Radial basis functions: Developments and applications to planetary scale flows

AMS Citation:
Flyer, N., and B. Fornberg, 2010: Radial basis functions: Developments and applications to planetary scale flows. Computers & Fluids, doi:10.1016/j.compfluid.2010.08.005.
Date:2010-08-10
Resource Type:article
Title:Radial basis functions: Developments and applications to planetary scale flows
Abstract: Radial basis functions (RBFs) can be seen as a major generalization of pseudospectral (PS) methods, abandoning the orthogonality of the basis functions and in return obtaining much improved simplicity and geometric flexibility. Spectral accuracy becomes now easily available also when using completely unstructured node layouts, permitting local node refinements in critical areas. The first major PDE applications for which RBFs have been shown to compete successfully against the best currently available numerical approaches can be found in the geosciences. Examples that are discussed here include translating vortex roll-ups (cyclogenesis), nonlinear flows on the sphere modeled by the shallow water equations, and 3D convection in the earth’s mantle.
Subject(s):Radial basis functions, RBF, Spherical geometry, Transport schemes, Shallow water equations, Mantle convection
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/d7q81djx
Publisher's Version: 10.1016/j.compfluid.2010.08.005
Author(s):
  • Natasha Flyer - NCAR/UCAR
  • Bengt Fornberg
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