Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (7): 827-838.doi: https://doi.org/10.1007/s10483-010-1317-7

• Articles • 上一篇    下一篇

Simple waves for two-dimensional compressible pseudo-steady Euler system

赖耕 盛万成   

  1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China
  • 收稿日期:2010-03-20 修回日期:2010-05-26 出版日期:2010-07-01 发布日期:2010-07-01

Simple waves for two-dimensional compressible pseudo-steady Euler system

 LAI Geng, CHENG Wan-Cheng   

  1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China
  • Received:2010-03-20 Revised:2010-05-26 Online:2010-07-01 Published:2010-07-01

摘要: A simple wave is defined as a flow in a region whose image is a curve in the phase space. It is well known that “the theory of simple waves is fundamental in building up the solutions of flow problems out of elementary flow patterns” see Courant and Friedrichs’s chassical book “Supersonic Flow and Shock Waves”. This paper mainly concerned with the geometric construction of simple waves for the 2D pseudo-steady compressible Euler system. Based on the geometric interpretation, the expansion or compression simple wave flow construction around a pseudo-stream line with a bend part are constructed. It is a building block that appears in the global solution to four contact discontinuities Riemann problems.

Abstract: A simple wave is defined as a flow in a region whose image is a curve in the phase space. It is well known that “the theory of simple waves is fundamental in building up the solutions of flow problems out of elementary flow patterns” see Courant and Friedrichs’s chassical book “Supersonic Flow and Shock Waves”. This paper mainly concerned with the geometric construction of simple waves for the 2D pseudo-steady compressible Euler system. Based on the geometric interpretation, the expansion or compression simple wave flow construction around a pseudo-stream line with a bend part are constructed. It is a building block that appears in the global solution to four contact discontinuities Riemann problems.

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