北京航空航天大学学报 ›› 2009, Vol. 35 ›› Issue (3): 356-360.

• 论文 • 上一篇    下一篇

格式中不同类型熵修正性能分析

周 禹, 阎 超   

  1. 北京航空航天大学 航空科学与工程学院, 北京 100191
  • 收稿日期:2008-03-11 出版日期:2009-03-31 发布日期:2010-09-16
  • 作者简介:周 禹(1981-),女,北京人,博士生,zhouyu@ase.buaa.edu.cn.
  • 基金资助:

    国防科学技术预先研究空气动力学资助项目(513130501)

Entropy correction analyses for Roe scheme

Zhou Yu, Yan Chao   

  1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2008-03-11 Online:2009-03-31 Published:2010-09-16

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: Muller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"Carbuncle"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.

Abstract: 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 Mach 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 case and diffuses the expansion shock completely as well. Harten-Hyman type-s entropy correction formulations do no contribution to shock case 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.

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