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一种改进的Roe格式及其稳定性分析

胡立军 赵昆磊

胡立军, 赵昆磊. 一种改进的Roe格式及其稳定性分析[J]. 应用数学和力学, 2020, 41(10): 1110-1124. doi: 10.21656/1000-0887.400388
引用本文: 胡立军, 赵昆磊. 一种改进的Roe格式及其稳定性分析[J]. 应用数学和力学, 2020, 41(10): 1110-1124. doi: 10.21656/1000-0887.400388
HU Lijun, ZHAO Kunlei. A Modified Roe Scheme and Stability Analysis[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1110-1124. doi: 10.21656/1000-0887.400388
Citation: HU Lijun, ZHAO Kunlei. A Modified Roe Scheme and Stability Analysis[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1110-1124. doi: 10.21656/1000-0887.400388

一种改进的Roe格式及其稳定性分析

doi: 10.21656/1000-0887.400388
详细信息
    作者简介:

    胡立军(1985—),男,博士(通讯作者. E-mail: hulijun@lsec.cc.ac.cn).

  • 中图分类号: O354|O241.82

A Modified Roe Scheme and Stability Analysis

  • 摘要: 低耗散的激波捕捉方法,包括流行的Roe格式,在计算多维强激波问题时会遭遇激波不稳定现象的困扰,这会严重影响格式对于高超声速流动问题的精确模拟.对Roe格式进行小扰动分析,结果表明:激波面纵向所有物理量的扰动均会衰减,而横向的密度扰动和剪切速度扰动不会衰减.在横向数值通量上增加与熵波和剪切波相对应的黏性来抑制Roe格式不稳定现象的发生.为了防止不合适的黏性影响格式对于接触间断和剪切层的分辨率,定义两个开关函数,使得黏性仅仅添加在激波层亚声速区的横向数值通量上.数值测试的结果表明:改进的Roe格式不仅保留了原始Roe格式高分辨率的优点,而且具有更好的鲁棒性,消除了激波不稳定现象.
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出版历程
  • 收稿日期:  2019-12-30
  • 修回日期:  2020-02-08
  • 刊出日期:  2020-10-01

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