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

The tar file circles.tar.gz contains the directories mentioned below.

Movies illustrating the mappings:

• Movie of the circle ... circlegridmovie.m
• Movie of the sphere ... spheregridmovie.m

Figure 3.1:

• Better version of Figure 3.1
• Matlab and Python scripts are in circles/grids/circle31
• Movie illustrating mapping

Figure 3.2: (Full grid versions)

• Figure 3.2(a) ... with colored lines as in Figure 3.1
• Figure 3.2(b)
• Figure 3.2(c)
• Figure 3.2(d)

Figure 4.1:

• Figure 4.1(a), grid on the sphere

Shallow water in starlike domain:

• Figure 8.4(a)
• Contour plots
• Contour plots with AMR
• Movie in color

Advection on the sphere:

• movie of advection on the sphere at constant angular velocity. 320x160 grid.
• movie of the same computation, shown in the rectangular computational domain.

Shallow water on the sphere:

• essentially 1-dimensional wave on the sphere
• comparison with 1d fine grid reference solution
• with AMR on the sphere

Acoustics in domain with circular inclusions:

• Figures from paper
• Comparisons to Cartesian grid on different domain

Turing model, pattern formation on the sphere:

• Movie of spots forming from random initial data