高分辨率差分格式的数值分析与限制因子的构造

基金项目: 国家自然科学基金

Numerical Analysis and Construction of Limiter of High Resolution Difference Scheme

Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China

摘要: 本文利用差分方法余项效应理论,分析比较了一些典型的限制因子.对不同的限制因子,格式的表现明显差异主要是由其数值耗散性、色散性强弱不同所致.在分析比较格式的数值耗散性、色散性之后,本文提出了一种新的限制因子,得到的格式在解的剧烈变化区具有更高的分辨率,在光滑区避免了由于数值色散性较强导致的失真.数值试验表明该格式具有较好的性质.
- 数值耗散 /
- 数值色散 /
- 限制因子
Abstract: In the paper,based on the theory of the remainder effects of difference schemes,some typical limiters are analysed and compared.For different limiters,the different strength of numerical dissipation and dispersion of schemes is the reason why theschemes show obvious different characteristics.After analysing and comparing thenumerical dissipation and dispersion of various schemes,a new kind of limiter isproposed.The new scheme has high resolution in sharp discontinuities,and avoids the "distortion" due to the stronger numerical dispersion in the relatively more smooth region.Numerical experiments show that the scheme has good properties.
- numerical dissipation /
- numerical dispersion /
- limiter

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