关于对流差分格式有界性与CBC准则的讨论

The Discussions of Relationship Between The Boundedness of Convective Schemes and Convection Boundedness Criterion (CBC)

通常认为CBC准则是差分格式有界性的充要条件。本文采用满足与不满足CBC准则的两种高阶差分格式对非线性问题进行了求解 ,重新讨论了格式有界性与CBC准则的关系 ,得出结论如下 :在数值方法稳定的前提下 ,CBC准则下的有界格式是求解有界的充分条件 ,而非必要条件 ;此外 ,文章还分析了张涵信三阶精度格式的特点。

There exists a conflicting issue of accuracy and boundedness among the convective schemes. The paper discusses the relationship between boundedness of the numerical solution and convection boundedness criterion by analyzing the characteristic of two high order schemes, the SMART scheme and Zhang Hanxin's third order scheme, where the SMART scheme meets convection boundedness criterion and Zhang's scheme does not. The conclusions have been drawn: (1) the CBC is a sufficient but unnecessary condition for achieving a solution of boundedness (2) Zhang Hanxin's third order scheme does not meet convection boundedness criterion.