Transport schemes on a sphere using radial basis functions

AMS Citation:
Flyer, N., and G. B. Wright, 2007: Transport schemes on a sphere using radial basis functions. Journal of Computational Physics, 226, 1059-1084, doi:10.1016/j.jcp.2007.05.009.
Date:2007-09-10
Resource Type:article
Title:Transport schemes on a sphere using radial basis functions
Abstract: The aim of this work is to introduce the physics community to the high performance of radial basis functions (RBFs) compared to other spectral methods for modeling transport (pure advection) and to provide the first known application of the RBF methodology to hyperbolic partial differential equations on a sphere. First, it is shown that even when the advective operator is posed in spherical coordinates (thus having singularities at the poles), the RBF formulation of it is completely singularity free. Then, two classical test cases are conducted: (1) linear advection, where the initial condition is simply transported around the sphere and (2) deformational flow (idealized cyclogenesis), where an angular velocity is applied to the initial condition, spinning it up around an axis of rotation. The results show that RBFs allow for a much lower spatial resolution (i.e. lower number of nodes) while being able to take unusually large time-steps to achieve the same accuracy as compared to other commonly used spectral methods on a sphere such as spherical harmonics, double Fourier series, and spectral element methods. Furthermore, RBFs are algorithmically much simpler to program.
Subject(s):Radial basis functions, Hyperbolic PDEs, Spherical geometry, Mesh-free
Peer Review:Refereed
Copyright Information:Copyright 2007 Elsevier.
OpenSky citable URL: ark:/85065/d79g5n2d
Publisher's Version: 10.1016/j.jcp.2007.05.009
Author(s):
  • Natasha Flyer - NCAR/UCAR
  • Grady Wright
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