对流热过程数值计算稳定性关系新探讨(Ⅰ)──耗散熵产非负定性分析

Investigations on the Relation of Numerical Stability of Fluid Dynamic Equations and Entropy Production of Dissipation(I) The Criterion of Non Negative Definite Property of Entropy Production of Dissipation

探讨性地定义了广义熵的概念；对于给定的模型方程，建立了相应的熵方程，揭示了模型方程潜在固有的耗散熵产非负定性质；提出了以该非负定性为准则，对模型方程的一般化数据格式稳定性限制条件的分析方法．针对一些典型的数值格式导出了具体的限制性条件，归纳性地显示该方法的结果为稳定性的充分条件。

An entropy in broad sense is suggested.The entropy equation is then deduced from a given model equation of advective diffusive problems.And it is displayed that the model equation has the non negative definite property of entropy production of dissipation.A general method which uses this property as the criterion to analyze the restrictive conditions of a general numerical scheme of the model equation is discussed.By the method,we can get the sufficient but not always necessary stability conditions for some typical numerical schemes in comparing with the classic conclusions.This article provides a new understanding of the intrinsic relations betwween the stability conditions and the entropy production of dissipation.