American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 355-364. doi: 10.3934/proc.2005.2005.355

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

Daniel Guo 1, and  John Drake 2,

1. 

Department of Mathematics and Statistics, University of North Carolina at Wilmington, Wilmington, NC 28403-3297, United States
2. 

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

Received  October 2004 Revised  March 2005 Published  September 2005

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, 86A1.
Citation: Daniel Guo, John Drake. A global semi-Lagrangian spectral model of shallow water equations with time-dependent variable resolution. Conference Publications, 2005, 2005 (Special) : 355-364. doi: 10.3934/proc.2005.2005.355
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