Improved smoothness and homogeneity of icosahedral grids using the spring dynamics method

An icosahedral grid that has both high smoothness and homogeneity is proposed. The grid-generation method is based on the combination of the spring dynamics (SPR) method with zero natural spring length (SPR0) and transformation by a smooth analytic function around the 12 vertices of an icosahedron. As a preliminary step, we first showed that the grid interval of the grid generated by SPR0 was inversely proportional to a Lambert conformal conic projection map factor, with a map angle of 300° around the vertices. Then, the transformation function was analytically determined, such that the resolution for the azimuthal direction became constant. In order to estimate cost-efficiency of numerical simulation with the newly proposed grid, we introduced an index defined as the ratio between the minimum grid interval and the squared maximum grid interval. It showed a 2.5% improvement from a recursive grid, and a 0.3–12% improvement from the best cases of the original SPR grid proposed by Tomita et al. (2002) [23] [hereafter, T02] dependent on global resolution. We also re-examined the original SPR method and found that the natural spring length proposed in T02 should be shortened to avoid instability when the global resolution is higher than grid-level 8. Finally, we examined the grids using advection/shallow water simulations.