Logically Rectangular Finite Volume Methods with Adaptive Refinement on the Sphere

Marsha J. Berger, New York University
Donna A. Calhoun, Commissariat à l’Energie Atomique (CEA)
Christiane Helzel, Ruhr-Universität Bochum
Randall J. LeVeque, University of Washington - Seattle Campus

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.