上风格式的若干性能分析

Characteristic analysis of the upwind scheme

采用理论分析和数值试验相结合的方法,对上风格式的三个典型代表:FDS、FVS及AUSM格式的性能进行了分析比较:FDS格式具有高的间断分辨率但可能出现非物理解;FVS格式捕捉强非线性波的能力很强,计算效率高,但耗散比较大;AUSM格式兼有高间断分辨率和高计算效率且克服了两者的弱点。以一维无粘激波管流场为算例考察了这些格式性能与间断分辨率。

The characteristics of three typical upwind schemes (FDS, FVS, AUSM) are analyzed and compared by combining theoretic analysis and numerical experiments. The FDS is an accurate scheme for discontinuities, but oscillations cannot be neglect in some cases; the FVS features exact capture of strong shock and efficiency at a cost of increased numerical dissipation; the AUSM is good at both accuracy and efficiency and overcomes their shortcomings. These characteristics are reviewed by simulating the inviscid shocktube problems.