对流热过程数值计算稳定性关系新探讨(Ⅱ)──一维平流差分方程的耗散熵产统计分析

Investigation on the Relation of Numerical Stability of Fluid Dynamic Equations and Entropy Production of Dissipation(Ⅱ)

试图探讨数值计算中数据分布形态的随机特性对数值稳定性的影响，针对ＦＴＣＳ，Ｌｅａｐｆｒｏｇ及隐式差分三种一维平流差分格式提出了耗散熵产的统计分析模型．对于ＦＴＣＳ及隐式差分格式，分析结果与Ｖｏｎ－Ｎｅｕｍａｎｎ方法分析结果完全一致；而对Ｌｅａｐｆｒｏｇ差分格式，分析结果是无条件中性稳定的，与Ｖｏｎ－Ｎｅｕｍａｎｎ法的分析结果有条件中性稳定，有一定差别．前人一些实际运算的确显示了数据分布的某些随机变化特性，进一步说明了统计分析的价值．

Abstract This article tries to explain the influence of the random property of the type of the data distrbution in numerical solutions on the numerical stability.A model of statistical analysis on entropy production of dissipation is suggested for FTCS,Leapfrog and implicit one dimensional convection difference schemes.For FTCS and implicit schemes,the results of the analysis are coincident with those of Von Neumann method;while for Leapfrog scheme,the result indicates that the scheme is unconditionally neurally stable,leaving some discrepancy with the result of Von Neumann method.Some