The effects of numerical viscosities. I: Slowly moving shocks (Q1924701)

We investigate the behavior of shock-capturing methods for slowly moving shocks. It is known that for slowly moving shocks even first-order schemes, such as the Godunov or Roe type methods, will generate downstream oscillatory wave patterns that cannot be effectively damped by the dissipation of these first-order schemes. The purpose of this paper is to understand the formation and behavior of these downstream patterns.