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Semi-Lagrangian advection on a spherical geodesic grid

✍ Scribed by Maria Francesca Carfora

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
390 KB
Volume
55
Category
Article
ISSN
0271-2091

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✦ Synopsis

Abstract

A simple and efficient numerical method for solving the advection equation on the spherical surface is presented. To overcome the well‐known ‘pole problem’ related to the polar singularity of spherical coordinates, the space discretization is performed on a geodesic grid derived by a uniform triangulation of the sphere; the time discretization uses a semi‐Lagrangian approach. These two choices, efficiently combined in a substepping procedure, allow us to easily determine the departure points of the characteristic lines, avoiding any computationally expensive tree‐search. Moreover, suitable interpolation procedures on such geodesic grid are presented and compared. The performance of the method in terms of accuracy and efficiency is assessed on two standard test cases: solid‐body rotation and a deformation flow. Copyright © 2007 John Wiley & Sons, Ltd.

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