Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (3): 753-763.doi: 10.1007/s10473-021-0308-9

• Articles • Previous Articles     Next Articles

THE VON NEUMANN PARADOX FOR THE EULER EQUATIONS

Li WANG   

  1. Department of Arts and Sciences, Shanghai Dianji University, Shanghai 201306, China
  • Received:2019-10-11 Revised:2020-03-03 Online:2021-06-25 Published:2021-06-07
  • About author:Li WANG,E-mail:wangli@sdju.edu.cn
  • Supported by:
    Supported by Academic Discipline Project of Shanghai Dianji University (16JCXK02) and Three campus Programs of Shanghai Dianji University (B1-0288-20-014-03-05).

Abstract: The reflection of a weak shock wave is considered using a shock polar. We present a sufficient condition under which the von Neumann paradox appears for the Euler equations. In an attempt to resolve the von Neumann paradox for the Euler equations, two new types of reflection configuration, one called the von Neumann reflection (vNR) and the other called the Guderley reflection (GR), are observed in numerical calculations. Finally, we obtain that GR is a reasonable configuration and vNR is an unreasonable configuration to resolve the von Neumann paradox.

Key words: von Neumann paradox, shock polar, Guderley reflection, von Neumann reflection

CLC Number: 

  • 35L65
Trendmd