Carbuncles as self-similar entropy solutions

TL;DR

This paper investigates carbuncles, instabilities in shock wave simulations, proposing they are a class of non-physical entropy solutions and analyzing their structure using a novel similarity coordinate technique.

Contribution

It introduces a new method to trigger and analyze carbuncles, suggesting they are non-physical entropy solutions rather than numerical artifacts.

Findings

Carbuncles can be characterized as self-similar entropy solutions.

A new technique effectively triggers and studies individual carbuncles.

Carbuncles are likely features of the continuum model, not just numerical errors.

Abstract

Numerical approximations of shock waves sometimes suffer from instabilities called carbuncles. Techniques for suppressing carbuncles are trial-and-error and lack in reliability and generality, partly because theoretical knowledge about carbuncles is equally unsatisfactory. It is not known which numerical schemes are affected in which circumstances, what causes carbuncles to appear and whether carbuncles are purely numerical artifacts or rather features of a continuum equation or model. This work presents evidence towards the latter: it is conjectured that carbuncles are a special class of non-physical entropy solutions. Using a new technique for triggering a single carbuncle, their structure is computed in detail in similarity coordinates.