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 " phenomen on. An analysis of the linearized form of the algorithms is carried out to explain and predict the generation of such instabilities. The information o btained is then used to design remedies that only slightly and locally modi fy the original schemes. (C) 2001 Academic Press.