Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains
by Donna A. Calhoun, Christiane Helzel, and Randall J. LeVeque, Submitted, 2006.

Shallow water on the sphere with AMR (Figures not in current draft of paper)

Directory listing

Movie on sphere

Movie in computational rectangle

Results on a 40x40 base grid with refinement factor 2 at level 2 and an additional factor of 4 at the finest level.

Time 0:

Time 0.8:

Time 1.6:

Time 0.8 in computational cooridnates:

Note: This computation was done on the domain [-3,1] x [-3,1] with the data in [-3,1] x [-1,1] reflected about (-1,-1) so that two copies of the sphere are covered. This takes twice the computation but has the advantage that the boundary conditions are then simply periodic in both directions, a situation that is handled automatically in AMRCLAW.

This problem can also be solved using AMR: amr/www/index.html

CLAWPACK Home page