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高超声速数值激波失稳的网格依赖性研究-2021增刊

任伟杰1,谢文佳1,田正雨2,张烨2,于航2   

  1. 1. 国防科技大学
    2. 国防科技大学空天科学学院
  • 收稿日期:2021-09-14 修回日期:2021-10-14 出版日期:2021-10-18 发布日期:2021-10-18
  • 通讯作者: 谢文佳
  • 基金资助:
    国家自然科学基金;国防科技大学校科研计划项目

Research on Grid Dependence of Hypersonic Numerical Shock Instability

  • Received:2021-09-14 Revised:2021-10-14 Online:2021-10-18 Published:2021-10-18
  • Contact: Wenjia Xie
  • Supported by:
    National Natural Science Foundation of China

摘要: 高超声速强激波的稳定捕捉仍然极具挑战性。目前,工程计算中普遍应用的数值格式在模拟多维强激波时通常会遭遇明显的激波不稳定现象。并且,数值格式的激波稳定性对计算网格表现出严重的依赖性。本文基于矩阵稳定性分析的方法,探究了计算网格对激波稳定性的影响规律。研究结果显示,在激波附近,通过增大网格长宽比或改变网格畸变角度可以有效改善激波捕捉的稳定性。并且,相比于增大网格长宽比,改变网格畸变角度提升激波捕捉稳定性的效果更加明显。在此基础上,结合数值耗散分析,对高马赫数下数值激波失稳现象的网格依赖性机理进行了探讨。

关键词: 有限体积法, 数值激波不稳定, 高超声速流动, 矩阵稳定性分析, 网格依赖性

Abstract: The stable capture of hypersonic strong shock waves is still extremely challenging. At present, the numerical scheme used in engineering calculations usually encounters obvious shock instability when simulating multi-dimensional strong shock waves. Moreover, the shock stability of the numerical scheme depends on the computational grid. Based on the method of matrix stability analysis, this paper explores the influence of computing grid on shock stability. The research results show that in the vicinity of the shock wave, increasing the grid aspect ratio or the grid distortion angle can effectively improve the stability of shock capture. Moreover, compared to increasing the grid aspect ratio, changing the grid distortion angle has a more obvious effect on improving the stability of shock capture. On this basis, combined with numerical dissipation analysis, the grid-dependent mechanism of numerical shock instability under high Mach number is discussed.

Key words: Finite volume method, Numerical shock instability, Hypersonic flow, Matrix stability analysis, Grid dependence

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