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guan yu fei xian xing ji suan wen ding xing de ruo gan wen ti
Author(s): 
Pages: 209-217
Year: Issue:  3
Journal: Chinese Journal of Theoretical and Applied Mechanics

Keyword:  非线性计算不稳定差分格式计算稳定性若干问题能量守恒守恒性非线性方程稳定性分析数值天气预报差分方程;
Abstract: Nonlinear computational instability is an important problem in numerical weather prediction. In last two years, several problems about nonlinear computational stability have been analysed and discussed for the typical one-dimensional nonlinear advectionequation u/t+ uu/x 0, two-dimensional vorticity equation ζ/t+ uζ/x + vζ/y = 0and nonlinear evolution equation F/t+ AF= 0. In this paper, some general discussionsare made, which include the concept, example and methods of analysis for nonlinear computational instability, the for its generation mechanism, measures to overcome it, and constructions of computationally stable difference schemes and so on. Particularly, the relations between computational stability and conservative property of energy are analysed. It is shown that schemes of complete quadrate conservation have perfectly computational stability. However if the artificial disspation term is not added to the schemes, nonlinear computational instability may occur even for "Lilly scheme" or "Arakawa scheme" of transient quadrate conservation that are widely adopted in numerical weather prediction, because conservative property of energy would be broken when leap-forg time difference is used. Besides, mathematically, there are often dis-eontinuty in the solution of nonlinear equation, and only generalized solution or weak solution can be obtained. However, the conservation of energy is not guaranteed for the weak solution.
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