A matrix stability analysis of the carbuncle phenomenon

  • Authors:

  • Michael Dumbser;Jean-Marc Moschetta;Jérémie Gressier

  • Affiliations:

  • Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, 70550 Stuttgart, Germany;SUPAERO, Department of Aerodynamics, 31400 Toulouse, France;ONERA, Department Models for Aerodynamics and Energetics, 31400 Toulouse, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

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.