面向全球大气模式的高精度算法研究

The high-order numerical schemes with specific considerations for atmospheric dynamics are of essential importance for developing the high-performance atmospheric general circulation models. In this research proposal, we plan to develop a novel numerical framework for global atmospheric modeling by using the multi-moment numerical approach, which has been originally developed by our group in the past years. This research mainly focuses on the following academic topics. First, a general principle for defining local degrees of freedom and constrained conditions will be established for the multi-moment constrained numerical schemes, which can be then used as a practical guidance to devise numerical formulation for global atmospheric modeling. Second, the proposed multi-moment schemes will be extended to spherical geometry with the application of the global grids of quasi-uniform grid spacing. Third, we are going to design a more efficient time integration method by implementing the high-order semi-implicit time integration scheme, which should be much more suitable for the atmospheric dynamics of multiple time scales. Particular attention will be paid to optimize the numerical model as a whole in respect of computational accuracy, efficiency and robustness for practical applications. This project concentrates on the key unsolved problems that prevents establishing high-performance numerical models for atmospheric dynamics on the complex spherical grids, which is currently one of the most active fields in the computational fluid dynamics researches. The numerical framework proposed in this project is based on the original work of the proposers, and the outcome can be expected to lead directly to the innovative progress in developing high-performance global atmosphere models.

根据大气运动特征和球面计算网格特点设计高精度算法是发展高性能全球大气模式的重要基础。本项目使用自主创新的多矩算法，在具有准均一网格距的球面网格上建立全新的全球大气模式数值框架。研究内容包括：第一，探索多矩算法中自由度及约束条件选取准则，提出适用于全球模式的高精度格式；第二，将多矩算法推广至具有准均一网格距的球面网格，发展多矩全球模式；第三，针对多时间尺度的大气运动设计高效的时间积分方法，发展高阶的半隐式积分格式。研究中综合考虑计算精度、效率和鲁棒性优化算法，保证所发展数值框架有良好的实用性。本项目围绕高阶格式构造及其在全球大气模式中应用的关键科学问题展开，是计算流体力学理论研究的前沿热点，有重要科学价值。本项目提出的数值框架具有自主知识产权，可直接用于高性能全球大气模式创新研究，为提高我国数值预报水平提供技术支持，有广阔的应用前景。

本项目针对发展高性能全球大气动力框架的关键问题开展研究工作，包括：高精度数值计算方法、准均匀球面网格和球面数值模式及大气模式时间积分方法研究。在本项目执行期间，项目组发展了基于通量重构的新高阶格式，研究了多矩格式模拟大气动力行为的性能，基于准均匀球面网格发展了全球模式，对比了不同准均匀网格应用在多矩模式中的特性并为三维动力框架中发展了水平显式-垂直隐式时间积分方法。相关研究成果已在本专业著名国际期Journal of Computational Physics, Quarterly Journal of the Royal Meteorological Society及Geoscientific Model Development等发表。