JFNK方法概述及其在大气全隐式非静力模式中的应用方案  

A Review of JFNK Methods and Its Applications in Atmospheric Non-Hydrostatical Model

作　　者：陈嘉滨[1] 纪立人[1] 陈长胜[2] 薛纪善[3] 

机构地区：[1]中国科学院大气物理研究所,北京100029 [2]南京信息工程大学大气科学系 [3]中国气象科学研究院,北京100081

出　　处：《大气科学》2006年第5期821-833,共13页Chinese Journal of Atmospheric Sciences

基　　金：国家自然科学基金资助项目40545020

摘　　要：首先介绍了近年来新发展的非线性方程全隐式数值求解的JFNK方法,及其在地球流体力学方面应用计算实例。可看到,无论在计算精度还是计算效率方面,全隐式数值求解远远超过常规的半隐式计算格式。其次,还讨论了JFNK方法在气象非静力模式中应用方案,并提出了用静力假定和半隐式差分格式来构造预条件处理器,变三维求解为二维求解,简化了方程组求解难度。该方案不仅可用于差分模式,也为用譜方法求解非静力模式提供可能。Over the last 10 years there have been major advances in supercomputing, which have triggered adoption of higher and higher resolution in atmospheric numerical models for various scales. And this in turn provides possibility and necessity to use implicit scheme and seek for its efficient algorithms. JFNK （Jaeobian-Free Newton-Krylov） method, a highly efficient method for solving the implicit nonlinear equation, has been successfully used in a number of fields of computational physics In this paper, the JFNK method and its application in geophysical flows are introduced. The JFNK method has been shown to be more efficient and accurate than the semi-implicit method for a given level of accuracy and a given CPU time. Preliminary results with the adveetion equation also show that even in the case of strong basic flow, the integration with the implicit scheme keeps well the features of the analytical solution, while apparent distortion occurs with the explicit or semi-implicit schemes. This paper also discusses the applications of the JFNK method in the atmospheric non-hydrostatic model. In a height-based terrain-following coordinate a set of implicit equations for the non-hydrostatic model is derived and the construction of preconditioner using hydrostatic relation and the semi-implicit method is proposed. And the problem solving the 3-D Helmholtz equation, which is commonly involved in non-hydrostatic model, can be reduced to a set of 2 D problems, thus releasing the difficulty of computation. The formulation can not only be used for the finite-difference models but also provide the possibility to use the spectral method in the non-hydrostatic models.

关 键 词：JFNK方法 非线性方程 预条件处理器 全隐式 非静力模式 

分 类 号：P435[天文地球—大气科学及气象学]