Acta mathematica scientia, Series B >
THE CARBUNCLE PHENOMENON IS INCURABLE
Received date: 2009-10-28
Online published: 2009-11-20
Numerical approximations of multi-dimensional shock waves sometimes exhibit an instability called the carbuncle phenomenon.
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 article presents evidence towards the latter: we propose that carbuncles are a special class of entropy solutions which can be physically correct in some circumstances. Using "filaments'', we trigger a single carbuncle in a new and more reliable way, and compute the structure in detail in similarity coordinates. We argue that carbuncles can, in some circumstances, be valid vanishing viscosity limits.
Trying to suppress them is making a physical assumption that may be false.
Key words： shock; Euler equation; carbuncle; entropy solution
Volker Elling . THE CARBUNCLE PHENOMENON IS INCURABLE[J]. Acta mathematica scientia, Series B, 2009 , 29(6) : 1647 -1656 . DOI: 10.1016/S0252-9602(10)60007-0
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