CARBUNCLE PHENOMENON - ON UPWIND SCHEMES IN MULTIDIMENSIONS

The purpose of this note is to provide some insight on and a cure to t he well-known 'carbuncle phenomenon'. The usual dimension by dimension extension of upwind schemes designed for the one-dimensional equation s of gas dynamics to the multidimensional equations yields poorly reso lved stationary (or slowly moving) shocks when applied to high Mach nu mber grid aligned flows on structured grids. We suggest that this phen omenon is due to inadequate crossflow dissipation offered by the usual approach. Here, we propose a parameter-free and easy to implement mul tidimensional, upwind dissipation that provides sufficient crossflow d issipation to alleviate the carbuncle pathology. The proposed approach also retains the desirable properties offered by one-dimensional upwi nding. Two numerical examples are considered for the purpose of compar ison.