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