Title: Geodynamo Simulation by Yin-Yang grid and Its Virtual Reality Visualization
Author: Akira Kageyama
Affiliation: Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology



The spherical shell is a key geometry in computational geoscience. The latitude-
longitude grid defined on the spherical coordinate system would be a natural choice 
for the computational grid due to its simple metrics and orthogonality. However, 
there are two kinds of numerical problems in the latitude-longitude grid: One is the 
coordinate singularity on the poles and the other is the grid convergence near the 
poles that imposes severe restriction on the Courant-Friedrichs-Lewy (CFL) condition 
there. Reviewing the latitude-longitude grid, one would notice that the two 
drawbacks of the latitude-longitude grid originate only from high latitude regions. The 
low latitude region near the equator, on the other hand, has rather desirable features 
for a base grid in the spherical geometry; it is orthogonal and its grid spacings are 
quasi-uniform. Suppose a sphere with unit radius and focus on the low latitude barrel-
like part with 90 degree between 45N and 45S around the equator. Cut off 1/4 of its 
longitude. Then, the remaining part of the barrel has an area of roughly a half of the 
full spherical surface. Based on this observation, we have proposed a new grid system 
for the spherical shell geometry, named Yin-Yang Grid.  The Yin-Yang Grid is a kind of 
the overset or Chimera grid, in which multiple grids are partially overlapped each other 
at their interfaces, covering all simulation region as a whole.  In the Yin-Yang Grid, we 
combine two identical grid systems (Yin and Yang) to cover a spherical surface.  The 
Yin or Yang grid is nothing but a part (roughly a half) of the latitude-longitude 
coordinates. The Yin-Yang grid is suited for massively parallel computers since the 
domain decomposition is straightforward. Using the Yin-Yang grid, we have developed 
new geodynamo code which achieved 15.2 Tflops on the Earth Simulator.

References: 
Akira Kageyama and Tetsuya Sato, The Yin-Yang Grid: An Overset Grid in Spherical 
Geometry, Geochem. Geophys. Geosyst., Q09005, doi:10.1029/2004GC000734, 
2004; preprint: arXiv: physics/0403123