Weather and climate numerical algorithms: An efficient, parallel solution scheme for the shallow water equations.

摘要

The rapid growth in the complexity of climate and weather simulation problems, combined with a paradigm shift from uniprocessor to parallel computing platforms, make the design of new numerical algorithms for climate and weather simulation essential. In this thesis, a numerical algorithm is developed that maps the global meteorological simulation problem onto massively parallel computer platforms efficiently and accurately through an understanding of the inter-relationships among the physics, the algorithm and the computing platform. The standard and well-accepted two dimensional nonlinear shallow water equation system is used as a model test problem. As part of the sequential algorithm, a conservative semi-implicit, Weak Lagrange-Galerkin (WLG) Finite Element (FE) scheme along with a novel quasi-uniform unstructured spherical triangular grid is designed and implemented. After a systematic evaluation of the true parallel complexity of meteorological simulation problems, an efficient, portable, scalable, parallel algorithm is developed. Sequential and parallel results from several benchmark problems of increasing complexity are presented and compared with published results. The present algorithm handles the pole problem, advection, Rossby waves and inertia-gravity waves accurately and efficiently. It achieves good parallel efficiencies on a range of parallel platforms. For these reasons, the present algorithm is a viable alternative to the currently popular spectral schemes.