非线性计算不稳定问题的进一步研究  

Farther Research on Nonlinear Computational Instability Problems

作　　者：季仲贞[1] 杨晓忠[1] 林万涛[1] 

机构地区：[1]中国科学院大气物理研究所大气数值模拟国家重点实验室,北京100029

出　　处：《中国科学院研究生院学报》2001年第1期59-65,共7页Journal of the Graduate School of the Chinese Academy of Sciences

基　　金：国家重点基础研究发展规划项目 (G19990 32 80 1) ;国家教育部高校骨干教师资助计划;国家自然科学基金 ( 49975 0 2 0 )共同资助项目

摘　　要：讨论了有关非线性计算不稳定的若干问题 ,其主要内容有 :(1 )考察了有代表性的三类发展方程 ,指出其对应的差分格式是否出现非线性计算不稳定 ,与原微分方程解的性质密切相关 ;(2 )进一步讨论了带周期边条件的守恒型差分格式的非线性计算稳定性问题 ,总结了克服非线性不稳定的有效措施 ;(3 )以非线性平流方程为例 ,着重分析了带非周期边条件的非守恒差分格式的非线性计算稳定性问题 ,给出了判别其计算稳定性的“综合分析判别法”Some new researchs on nonlinear computational instability are introduced, the contents are as follows: (1) Three types of representative evolution equations are analyzed, and the close relationship between the nonlinear computational stability and instability of their corresponding difference the properties of their solution is revealed; (2) Nonlinear computation instability problem of conservative difference equations with nonperiodic boundary conditions is further discussed, and some effective ways to avoid nonlinear computation instability are included; (3)Nonlinear computation instability problem of nonconservative difference equations with aperiodic boundary condition is focused on by using nonlinear advection equations as examples, and 'synthetically analysis method' is given to judge their computation stability.

关 键 词：非线性 计算稳定性 非守恒格式 非周期边条件 差分格式 微分方程 发展方程 

分 类 号：O175.13[理学—数学]