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2003, Volume 2003: 375-385. Doi: 10.3934/proc.2003.2003.375 open access
This issue Previous Article Modified Chebyshev rational spectral method for the whole line Next Article Lorentz geometry technique in nonimaging optics

A global semi-Lagrangian spectral model for the reformulated shallow water equations

  • 1.

    Department of Mathematics and Statistics, University of North Carolina at Wilmington, Wilmington, NC 28403-3297

  • 2.

    Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831

Received:  August 31, 2002
Revised:  January 31, 2003
Published:  March 2003
Abstract Related Papers Cited by
    Abstract
  • In this paper, we study the semi-Lagrangian spectral method for the shallow-water equations in a rotating, spherical geometry. With the reformulation of a vector calculus identity for spherical geometries, we are able to write the vorticity and divergence equations in advective form and directly apply the semi-Lagrangian, spectral method. The scalar vorticity and divergence equations are used to avoid the pole problems. Shape preserving interpolation is used for the calculation of departure point values for all fields. The results of the standard test set are presented showing accuracy, stability and regularity properties of the method for atmospheric flows.
    Mathematics Subject Classification: Primary: 35Q35, 65Q99, 76M22, 86A10.

    Citation:
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