A note on the convergence of Godunov type methods for shock reflection problems

This paper identifies a new pathology that can be found for numerical simulations of nonlinear conservation law systems. Many of the difficulties already identified in the literature (rarefaction shocks, carbuncle phenomena, slowly moving shocks, wall heating, etc.) can be traced to insufficient numerical dissipation, and the current case is no different. However, the details of the case we study here are somewhat unique in that the solution which is found by the numerics can fail to have a derivative anywhere in the post-shock region.