地球流体力学数值方法的若干研究

Several Studies about the Numerical Methods to Geophysics Fluid Dynamics

本文简要综述了三十多年来中科院大气物理所发展的一些地球流体力学数值方法及有关问题的研究。其中包括用物理观点和数学分析相结合的方法阐述造成计算紊乱和计算不稳定的机理 ;论证计算稳定性与算子非负性和能量守恒性之间的密切关系 ;对国际上流行的瞬时能量守恒的格式找到非线性计算不稳定的特解 ;设计出一批内部协调并且具有完全平方守恒性的差分格式 (包括隐式的、显式的和高精度的 ) ;发展了多种经济省时算法等等。

In this paper, some numerical methods of geophysical fluid dynamics and relative problems, which were developed by IAP in past thirty years, are briefly introduced. This paper explains the mechanism of computational disorder and instability from both physical and mathematical opinions and discusses the close relationship among computational stability, non negative of operators and energy conservation, The finding of the nonlinear unstable solution of some internationally popular instantaneous energy conservation schemes and design of a series of explicit, implicit and high resolution schemes which are completely squarely conservative and harmonic inside are presented. The development of many economic algorithms is described etc.. In addition, some applications of thealgorithms in typhoon track simulation, etc., are briefly introduced.