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