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Keywords:

  • Flux vector splitting;
  • positivity of pressure;
  • compressible flow;
  • supersonic;
  • contact and shear waves;
  • carbuncle.

Abstract

The AUFS scheme by Sun and Takayama is a flux splitting scheme without breakdown of discrete shock profiles, usually called carbuncle, but still with a good resolution of entropy waves. Unfortunately, numerical tests with this scheme yield that the viscosity on entropy waves is too small while the viscosity on shear waves is too large. In this paper, we prove that both deficiencies are inherent to the construction of the scheme and provide fixes to overcome them.