Heuristical and numerical considerations for the carbuncle phenomenon

TL;DR

This paper investigates the carbuncle phenomenon in numerical simulations, identifying key sources and proposing stabilization methods to mitigate it, through experiments and heuristic analysis.

Contribution

It introduces a detailed analysis of the carbuncle's causes and suggests higher order methods as a stabilization approach.

Findings

Instability of 1d shock position contributes to carbuncle.

Low numerical viscosity on shear waves is a key factor.

Higher order methods help stabilize shocks and reduce carbuncle.

Abstract

In this study, we investigate the so called carbuncle phenomenon by means of numerical experiments and heuristic considerations. We identify two main sources for the carbuncle: instability of the 1d shock position and low numerical viscosity on shear waves. We also describe how higher order stabilizes the 1d shock position and, thus, reduces the carbuncle.