An energy-dissipative remedy against carbuncle: Application to hypersonic flows around blunt bodies

The carbuncle phenomenon is a critical numerical instability preventing the accurate simulation of hypersonic flows around blunted configurations. After reviewing the known remedies to handle numerically this instability (designed, all of them, for Finite Volume methods), we present and analyze in depth the only effective cure reported in literature for Residual Distribution schemes.

The shock fix, which is formulated as a locally active artificial diffusive term, depends on a single controlling parameter ϵs. Extensive testing of the fix in combination with the Residual Distribution technique allows for the determination of an optimal value for ϵs, which can be related to a local Péclet-like number.

After testing the performance of the fix in combination with the Residual Distribution technique it was originally designed for, the flexibility of the fix is demonstrated by coupling it with a cell-centered Finite Volume discretization: carbuncle instabilities are equally avoided in this case.

Finally, a number of limitations identified in the first testing phase lead to the derivation of a more physically consistent, energy dissipative family of carbuncle fixes, whose improved capabilities are demonstrated.