Abstract. The logically rectangular finite volume grids for two-dimensional PDEs on the sphere and for three-dimensional problems in a spherical shell recently introduced by Calhoun, Helzel, and LeVeque have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the GeoClaw software and demonstrate well-balanced methods that exactly maintain equilibrium solutions, such as shallow water equations for an ocean at rest over arbitrary bathymetry.
Keywords. shallow water equations, sphere, finite volume, adaptive mesh refinement, well-balanced schemes, bathymetry
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Tar file of code producing Figures 6 and 7
bibtex entry:
@article{mjb-dac-ch-rjl:amrsphere09,
author = "M. J. Berger and D. A. Calhoun and C. Helzel and R. J. LeVeque",
title="Logically rectangular finite volume methods
with adaptive refinement on the sphere ",
journal= "Phil. Trans. R. Soc. A",
year="2009",
pages="to appear"
}