Article
Logically Rectangular Finite Volume Methods with Adaptive Refinement on the Sphere
Philosophical Transactions of the Royal Society A
(2009)
Abstract
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.
Keywords
- shallow water equations,
- sphere,
- finite volume,
- adaptive mesh refinement,
- well-balanced schemes,
- bathymetry
Disciplines
Publication Date
November, 2009
Citation Information
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 Vol. 367 Iss. 1907 (2009) Available at: http://works.bepress.com/donna_calhoun/2/