Logically Rectangular Finite Volume Methods with Adaptive Refinement on the Sphere
The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently 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.
Marsha J. Berger, Donna A. Calhoun, Christiane Helzel, and Randall J. LeVeque. "Logically Rectangular Finite Volume Methods with Adaptive Refinement on the Sphere" Philosophical Transactions of the Royal Society A 367.1907 (2009): 4483-4496.
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