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<p>We are intrigued by the issues of shock instability, with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it. For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components, such as a disturbed one-dimensional (1D) steady shock wave, we conduct a formal asymptotic analysis for the Euler system and associated numerical methods. This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms. Furthermore, a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms. To verify the stability mechanism, a consistent, low-dissipation, and shock-stable HLLC-type Riemann solver is presented.</p>

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A low Mach number asymptotic analysis of dissipation-reducing methods for curing shock instability

  • 期刊论文

  • 发表日期：

    2025年4月3日

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  • Hongping Guo,
  • Xun Wang,
  • Zhijun Shen

摘要

We are intrigued by the issues of shock instability, with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it. For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components, such as a disturbed one-dimensional (1D) steady shock wave, we conduct a formal asymptotic analysis for the Euler system and associated numerical methods. This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms. Furthermore, a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms. To verify the stability mechanism, a consistent, low-dissipation, and shock-stable HLLC-type Riemann solver is presented.