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 50 (2008), 723-752.

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