Carbuncles as self-similar entropy solutions

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.