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A global semi-Lagrangian spectral model of shallow water equations with time-dependent variable resolution

Pages: 355 - 364, Issue Special, August 2005

 Abstract        Full Text (189.3K)              

Daniel Guo - Department of Mathematics and Statistics, University of North Carolina at Wilmington, Wilmington, NC 28403-3297, United States (email)
John Drake - Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States (email)

Abstract: A time-dependent focusing grid works together with the formulation of a semi-implicit, semi-Lagrangian spectral method for the shallow-water equations in a rotated and stretched spherical geometry. The conformal mapping of the underlying discrete grid based on the Schmidt transformation, focuses grid on a particular region or path with variable resolution. A new advective form of the vorticity-divergence equations allows for the conformal map to be incorporated while maintaining an efficient spectral transform algorithm. A shallow water model on the sphere is used to test the spectral model with variable resolution. We are able to focus on a specified location resolving local details of the flow. More importantly, we could follow the features of the flow at all time.

Keywords:  Semi-Lagrangian Method; Spectral Transformation; Shallow-Water Equations; Time-Dependent; Variable Resolution; Standard Test Cases.
Mathematics Subject Classification:  Primary: 30C30, 35Q35, 65M70, 65T50, 86A10.

Received: October 2004;      Revised: March 2005;      Published: September 2005.