Tangential artificial viscosity to alleviate the carbuncle phenomenon, with applications to single-component and multi-material flows

This paper describes a novel approach to alleviate the carbuncle phenomenon which consists in adding to any carbuncle prone Riemann solver an extra viscosity term in tangential momentum flux and its contribution to the energy conservation equation. This term contains one numerical parameter only, a scalar viscosity, which is reduced using a face-based shear detector to preserve shear waves. The idea stems from the investigation of some of the existing Riemann solvers, also presented in the paper. Indeed, when splitting the numerical flux into the face normal and tangential components, we observe that all the carbuncle free Riemann solvers present in the tangential part a numerical viscosity which scales with the sound speed when the normal flow velocity becomes zero. Opposite, in the carbuncle prone solvers this viscosity scales with the normal flow velocity. In particular the carbuncle free HLLCM scheme proposed by Shen et al. can be written by adding to the carbuncle prone HLLC scheme a tangential artificial viscosity term. Then the same can be done for any other Riemann solver, which renders the approach easy to implement in CFD codes for compressible flows. Numerical experiments shows the efficiency of the approach in computing carbuncle free single-component and multi-material flows. •Some Riemann solvers are investigated by splitting their numerical flux into interface normal and tangential components.•The carbuncle free ones present a tangential viscosity which scales with the sound speed as the normal velocity vanishes.•A tangential artificial viscosity approach is then proposed to alleviate the carbuncle problem to any Riemann solver.•The approach, combined with a shear sensor to preserve shear waves, is easy to implement in CFD codes.