Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon

Some upwind formulations promote severe instabilities that originate in the numerical capturing of shocks; this is known as the “carbuncle” phenomenon. An analysis of the linearized form of the algorithms is carried out to explain and predict the generation of such instabilities. The information obtained is then used to design remedies that only slightly and locally modify the original schemes.