面向高分辨率大气模式的快速与稳定数值方法研究

项目名称： 面向高分辨率大气模式的快速与稳定数值方法研究

项目编号： No.41205072

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 大气科学学科

项目作者： 徐世明

作者单位： 清华大学

项目金额： 25万元

中文摘要： 高分辨率大气模式是近期气候模式和天气预报模式的主要发展趋势，基于有限差分法和经纬网格的大气模式动力框架具有可直观反应大气运动的基本特征，易于保证能量守恒等优点，但随着分辨率逐渐提高，显式积分算法面临着时间步长受限、计算效率下降等问题，渐渐成为制约有限差分和模式应用的瓶颈。本课题提出以GAMIL为平台，设计针对高分辨率（0.1度）的快速稳定数值算法，满足积分步长超过30秒和完全平方守恒等特性。根据快慢分离的原则，将高分辨率下影响稳定性和时间步长的快过程（如重力波）进一步纳入半隐式求解范畴，形成大规模代数系统求解和显式积分相结合的平方守恒数值方法。通过高性能并行直接求解算法、迭代算法以及多时步信息重用算法的的研发，提升框架程序的性能和可扩展性。此项目对于高分辨率GAMIL大气模式和FGOALS_g耦合模式的发展，以及国内自主研制框架的发展将起到积极的推动作用。

中文关键词： 大气模式动力框架；多重网格算法；切比雪夫迭代；施瓦茨克里斯托夫映射；网格生成

英文摘要： High resolution atmospheric model is current trend for the models used for both Climate Study and Numerical Weather Prediction. Atmospheric models based on lat-lon grid and finite difference method have the advantage of high efficiency, easy implementation and easy maintenance of conservation of energy. But for higher resolution, due to the existence of poles, these models face the problem of limited time step size and low efficiency. This has become a main obstacle for the further development in the era of high resolution models. Based on semi-implicit time integration, we propose the development of supporting numerical algorithms for dynamic core of high resolution atmospheric models. These algorithms are both fast and designed to feature good numerical stability, supporting resolution up to 0.5 degree to 0.1 degree and time steps over 30 seconds. The fast processes which affect time step and numerical stability, such as gravity wave，are treated with an implicit method. Therefore, large scale linear systems are formed which are treated with direct methods or Krylov-subspace iterative methods. Also we propose the use of multi-step techniques to reuse matrix factorizations or preconditioners to further reduce computation overhead involved in linear system solving. Implementation on cluster-based parallel archite

英文关键词： Dynamic Core；Multigrid Algorithm；Chebyshev Iteration；Schwarz-Christoffel Mapping；Grid Generation