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

Daniel Guo; John Drake

doi:10.3934/proc.2003.2003.375

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2003, Volume 2003: 375-385. Doi: 10.3934/proc.2003.2003.375 open access

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

Daniel Guo^1, and
John Drake^2,

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

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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.

Keywords:

Semi-Lagrangian Method; Spectral Transformation; Shallow-Water Equations; Standard Test cases.

Mathematics Subject Classification: Primary: 35Q35, 65Q99, 76M22, 86A10.

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