A deep non-hydrostatic compressible atmospheric model on a Yin-Yang grid

The singularity in the traditional spherical polar coordinate system at the poles is a major factor in the lack of scalability of atmospheric models on massively parallel machines. Overset grids such as the Yin-Yang grid introduced by Kageyama and Sato [1] offer a potential solution to this problem. In this paper a three-dimensional, compressible, non-hydrostatic atmospheric model is developed and tested on the Yin-Yang grid building on ideas previously developed by the authors on the solution of Elliptic boundary value problems and conservation on overset grids. Using several tests from the literature, it is shown that this model is highly stable (even with little off-centering), accurate, and highly efficient in terms of computational cost. The model also incorporates highly efficient and accurate approaches to achieve positivity, monotonicity and conservative transport, which are paramount requirements for any atmospheric model. The parallel scalability of this model, using in excess of 212 million unknowns and more than 6000 processors, is also discussed and shown to compare favourably with a highly optimised latitude-longitude model in terms of scalability and actual run times.