计算地球流体力学的回顾、进展及展望

THE COMPUTATIONAL GEOPHYSICAL FLUID DYNAMICS: REVIEW, PROGRESS AND PROSPECT

简要回顾了计算地球流体力学的发展历史,概括介绍了计算地球流体力学的研究进展及最新发展方向。针对线性发展方程的计算稳定性问题,介绍了判定线性发展方程初值问题的稳定性判别条件:CLF条件。对分析线性偏微分方程差分格式计算稳定性判据的Fourier方法、启发性稳定性分析方法,也做了简要的介绍。同时,重点介绍了判定线性发展方程初边值问题计算稳定性的GKS理论。在非线性发展方程的计算稳定性方面,重点介绍的主要内容包括:非线性发展方程的计算紊乱现象和计算不稳定的原因;克服非线性发展方程计算不稳定的方法;瞬时平方守恒型差分格式的构造;隐式和显式完全平方守恒格式的设计;强迫耗散非线性发展方程的计算稳定性问题。在计算地球流体力学的近期进展方面,重点介绍了非线性发展方程的计算稳定性与初值的关系,强迫耗散非线性发展方程显式准完全平方守恒格式的构造。对计算地球流体力学需要进一步研究的问题,也做了简要介绍。这些研究工作的介绍,无疑对推动计算地球流体力学的研究和大气海洋模式的研制具有一定的指导意义。

The developed history of computational geophysical fluid dynamics is simply reviewed and its research progress and latest developing direction is briefly introduced. For the computational stability of linear evolution equation, the condition of CLF for judging the computational stability of initial value problem is introduced. The Fourier method and heuristic stability theory for the analysis of the computational stability criterion of the difference scheme of linear partial differential equation are also briefly introduced. Furthermore, the GKS theory for judging the initial-boundary value problem of linear evolution equation is emphatically discussed. For the computational stability of nonlinear evolution equation, the contents are: the mechanism of computational disorder and instability, the method for solving instability, the construction of instantaneous square conservation scheme, the design of implicit and explicit complete square conservation scheme and the computational stability of forced dissipative nonlinear evolution equation. In the near future progress of computational geophysical fluid dynamics, the relationship between the computational stability and the initial value of nonlinear evolution equation and the construction of explicit quasi-complete square conservation scheme of forced dissipative nonlinear evolution equation are emphatically presented. A brief discussion is given to the problems that needs further study of computational geophysical fluid dynamics. The presentation of the research has undoubtedly guidance for the study of computational geophysical fluid dynamics and the development of atmospheric and oceanic model.