Caption: Quadrilateral grids on the circle and the sphere. In each case the computational domain is a rectangular grid.
Movies illustrating the mappings:
For more information:
These mappings and related mappings are discussed further in the paper Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains by Donna A. Calhoun, Christiane Helzel, and Randall J. LeVeque (In preparation)
Advection on the sphere: