数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (6): 1647-1656.doi: 10.1016/S0252-9602(10)60007-0

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THE CARBUNCLE PHENOMENON IS INCURABLE

 Volker Elling   

  1. Department of Mathematics, University of Michigan, MI4810-1043, USA
  • 收稿日期:2009-10-28 出版日期:2009-11-20 发布日期:2009-11-20

THE CARBUNCLE PHENOMENON IS INCURABLE

 Volker Elling   

  1. Department of Mathematics, University of Michigan, MI4810-1043, USA
  • Received:2009-10-28 Online:2009-11-20 Published:2009-11-20

摘要:

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.

关键词: shock, Euler equation, carbuncle, entropy solution

Abstract:

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

中图分类号: 

  • 74S10