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.
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.
Marsha J
MJ
Berger
Donna A
DA
Calhoun
Christiane
C
Helzel
Randall J
RJ
LeVeque