Applied Mathematics Commons^™

Logically Rectangular Finite Volume Methods With Adaptive Refinement On The Sphere, Marsha Berger, Donna Calhoun, Christiane Helzel, Randall Leveque

Donna Calhoun

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.