Abstract
The purpose of this note is to provide some insight on and a cure to the well-known ‘carbuncle phenomenon’. The usual dimension by dimension extension of upwind schemes designed for the one-dimensional equations of gas dynamics to the multidimensional equations yields poorly resolved stationary (or slowly moving) shocks when applied to high Mach number grid aligned flows on structured grids. We suggest that this phenomenon is due to inadequate crossflow dissipation offered by the usual approach. Here, we propose a parameter-free and easy to implement multidimensional, upwind dissipation that provides sufficient crossflow dissipation to alleviate the carbuncle pathology. The proposed approach also retains the desirable properties offered by one-dimensional upwinding. Two numerical examples are considered for the purpose of comparison.
Published Version
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