Roe格式中不同类型熵修正性能分析  

Entropy correction analyses for Roe scheme

作　　者：周禹[1] 阎超[1] 

机构地区：[1]北京航空航天大学航空科学与工程学院,北京100191

出　　处：《北京航空航天大学学报》2009年第3期356-360,共5页Journal of Beijing University of Aeronautics and Astronautics

基　　金：国防科学技术预先研究空气动力学资助项目(513130501)

摘　　要：针对Roe格式中较为流行的3类熵修正:Muller型、Harten-Yee型和Harten-Hyman型熵修正,从理论分析入手,辅以Euler方程为控制方程的激波管问题,前台阶流动和运动激波的双马赫反射3个数值实验,对不同熵修正的性能做了深入研究,得出如下结论:Mull-er型和Harten-Yee型熵修正方法作用于激波和非物理的膨胀激波2种情况:激波情况下引入的数值耗散,能根本改善"Carbuncle"现象,膨胀激波时其数值粘性也足以使膨胀激波得以耗散;而类Harten-Hyman型熵修正只对膨胀过程起修正作用,对激波情况无效,不能改善"Car-buncle"现象,该类熵修正的数值粘性较小,不足以使膨胀过程正确求解;直接采用δ值代替特征值的特征值修正方法效果好于传统的特征值修正方法.Three types＇ entropy fix formulations for the Roe scheme were analyzed in theory and assessed by three numerical tests which were shock tube problem, step flow and double Maeh reflection. The results show that ＂Carbuncle phenomena＂ occurs when capturing strong shock because of the original Roe scheme＇s numerical instability. Muller＇s and Harten-Yee＇s entropy fix methods introduce numerical dissipation to both shock and non-physical expansion shock processes. The numerical dissipation improves the Roe scheme＇s numerical stability and cures ＂ Carbuncle phenomena＂ entirely for shock ease and diffuses the expansion shock completely as well. Harten-Hyman type＇s entropy correction formulations do no contribution to shock ease and can not cure the ＂Carbuncle phenomena＂. They can only fix non-physical expansion processes partially because their numerical dissipation is not large enough. The eigenvalue correction method which directly uses delta replace eigenvalue itself exceeds the traditional method.

关 键 词：计算流体力学 数值分析 激波 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]