American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 375-385. doi: 10.3934/proc.2003.2003.375

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  September 2002 Revised  February 2003 Published  April 2003

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, 86A1.
Citation: Daniel Guo, John Drake. A global semi-Lagrangian spectral model for the reformulated shallow water equations. Conference Publications, 2003, 2003 (Special) : 375-385. doi: 10.3934/proc.2003.2003.375
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