On the plane wave Riemann Problem in Fluid Dynamics

TL;DR

This paper analyzes the stability of plane-wave Riemann problems in 2D fluid dynamics, revealing contact discontinuity instability and its implications for numerical methods and related instabilities.

Contribution

It provides a stability analysis showing contact discontinuities are unstable under perturbations and links this to numerical instabilities like carbuncle.

Findings

Contact discontinuity is unstable under perturbations.

Numerical post shock noise can trigger contact instability.

Relation to carbuncle instability is established.

Abstract

The paper contains a stability analysis of the plane-wave Riemann problem for the two-dimensional hyperbolic conservation laws for an ideal compressible gas. It is proved that the contact discontinuity in the plane-wave Riemann problem is unstable under perturbations. The implications for Godunovs method are discussed and it is shown that numerical post shock noise can set of a contact instability. A relation to carbuncle instabilities is established.