A matrix stability analysis of the carbuncle phenomenon
A matrix stability analysis of the carbuncle phenomenon
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DOI：
10.1016/j.jcp.2003.12.013
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发表时间：
2004-07
影响因子：
4.1
通讯作者：
M. Dumbser;J. Moschetta;J. Gressier
中科院分区：
文献类型：
--
作者：
M. Dumbser;J. Moschetta;J. Gressier
蜂窝现象是一种激波不稳定机制，它破坏了使用低耗散迎风格式计算网格对齐激波的所有努力。本文基于矩阵方法，在结构网格上对二维定常激波进行了稳定性分析。相应特征值问题的数值解证实了不稳定模态的典型奇偶形式，并显示了计算中目前观察到的马赫数阈值效应。此外，本方法还表明，定常激波的不稳定性不仅取决于上游马赫数，而且还取决于数值激波结构。最后，不稳定性的来源是本地化的上游地区，提供了一些线索，以更好地了解和控制的发病痈。
The carbuncle phenomenon is a shock instability mechanism which ruins all efforts to compute grid-aligned shock waves using low-dissipative upwind schemes. The present study develops a stability analysis for two-dimensional steady shocks on structured meshes based on the matrix method. The numerical resolution of the corresponding eigenvalue problem confirms the typical odd–even form of the unstable mode and displays a Mach number threshold effect currently observed in computations. Furthermore, the present method indicates that the instability of steady shocks is not only governed by the upstream Mach number but also by the numerical shock structure. Finally, the source of the instability is localized in the upstream region, providing some clues to better understand and control the onset of the carbuncle.