Carbuncle Computational Fluid Dynamics Problem for Blunt-Body Flows

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Carbuncle Computational Fluid Dynamics Problem for Blunt-Body Flows

MacCormack, Robert W.

A key problem that has remained unsolved for the past quarter-century is presently compromising the accuracy of heat transfer predictions made by numerical simulations of hypersonic flow. This numerical difficulty is called the carbuncle problem, a local unpleasant displacement of the bow shock wave shape. It is most prominent in computational fluid dynamics simulations within the blunt nose region of an aerodynamic vehicle on axisymmetric grids. Most efforts to remedy this problem have concerned the numerical treatment of the bow shock wave: both the algorithm calculating the discontinuities across the bow shock wave and the alignment of the computational mesh with the shock wave location. Although these efforts have improved simulation accuracy, none have yet removed the problem. The fundamental requirement of any numerical procedure is that it has sufficient numerical dissipation to control error growth. All methods contain it, and an unintended consequence will be shown to be its contribution to the carbuncle problem. This paper will analyze solution algorithm procedures, in particular their inherent numerical dissipation and application on axisymmetric grids, to determine the cause of and remedy for the carbuncle problem.