Affordable shock-stable item for Godunov-type schemes against carbuncle phenomenon

The work proposes a simple, efficient and unified approach to combat carbuncle phenomenon. The basic idea of this approach is to construct an affordable shock-stable item into numerical flux. This item is acquired by comparing three-wave Roe solver and two-wave HLL solver based on Roe linearization and the projection of difference term. It is consistent with shear viscosity and meantime restrained by the pressure-based sensing function for shear layer. The proposed enhancement is easy to implement and apply within Roe, HLLEM, HLLC, AUSM+, etc. Several well-known cases illuminate its shock robustness and potential application to hypersonic flows.