差分格式余项效应分析及格式的改造和优化

利用差分格式的ＭｏｄｉｆｉｅｄＰＤＥ，对差分格式的余项效应进行了系统的分析．其方法比Ｆｏｕｒｉｅｒ方法更直接、全面和具有构造性．利用所导出的数值耗散关系和色散关系，可对格式的稳定性质、耗散和色散性质，以及群速度效应进行改造，并为设计高效能、高分辨率格式指出了方向．此外，以某些不稳定格式的改造为例，进一步证明了方法的效能．

The Remainder-effect Analysis of FDS and the Applications to Reforming or Optimazing for FDS

In this paper,the remainder-effect analysis method for finite difference schemes is systematically discussed using the Modified-PDE approach. This method is more rigorous,direct,complete and construstive than the Fourier method.By use of the numerical dissipation relation and dispersion relation,either the character analysis,such as the stability,the dissipation and dispersion effect,the numerical group velocity effect,or the reforming and optimazing for finite difference schemes may be accomplished and performed. Especially,the design direction of high function or high resolution scheme can be found from the remainder-effect analysis.Finally,some"bad"schemes are successfully reformed and optimazed.The results further prove the effectiveness of the method.