A Hybrid Numerical Method to Cure Numerical Shock Instability

Abstract

In this note, we propose a new method to cure numerical shock instability by hybriding different numerical fluxes in the two-dimensional Euler equations. The idea of this method is to combine a "full-wave" Riemann solver and a "less-wave" Riemann solver, which uses a special modified weight based on the difference in velocity vectors. It is also found that such blending does not need to be implemented in all equations of the Euler system. We point out that the proposed method is easily extended to other "full-wave" fluxes that suffer from shock instability. Some benchmark problems are presented to validate the proposed method.