Dissection of a Sphere and Yin-Yang Grids

A geometrical dissection that divides a spherical surface into two identical pieces is considered. When the piece is symmetric in two perpendicular directions, the two pieces are called yin and yang and the dissection is yin-yang dissection of a sphere. The yin and yang are mapped each other by a rotation M on the sphere where M2 = 1. Therefore, the yin’s landscape viewed from yang is exactly the same as the yang’s landscape viewed from yin, and vice versa. This complemental nature of the yin-yang dissection leads to the idea of new spherical overset grid named Yin-Yang grid. The flexibility of the yin-yang dissection of a sphere enables one to patch the piece with an orthogonal, quasi-uniform grid mesh. Since the two pieces are identical, one computational routine that involves individual calculation in each grid is used for two times, one for yin grid and another for yang. Other routines that involve data transformation between yin and yang are also recycled for two times because of the complemental nature of the grids. Due to the simplicity of the underlying grid geometry, the Yin-Yang grid suits to massively parallel computers.