The Riemann solutions comparison for compressible Euler equations in different Chaplygin gas states

2021 ◽  
pp. 1-15
Author(s):  
Weifeng Jiang ◽  
Tong Li ◽  
Zhen Wang ◽  
Tingting Zhang
Keyword(s):  
Euler Equations ◽  
Chaplygin Gas ◽  
Compressible Euler Equations ◽  
Riemann Solutions ◽  
Compressible Euler

scholarly journals EXACT RIEMANN SOLUTIONS TO COMPRESSIBLE EULER EQUATIONS IN DUCTS WITH DISCONTINUOUS CROSS-SECTION

2012 ◽  
Vol 09 (03) ◽  
pp. 403-449 ◽  
Author(s):  
EE HAN ◽  
MAREN HANTKE ◽  
GERALD WARNECKE
Keyword(s):  
Initial Data ◽  
Euler Equations ◽  
Cross Section ◽  
Phase Plane ◽  
Compressible Euler Equations ◽  
Crucial Point ◽  
Riemann Solutions ◽  
Compressible Euler ◽  
Velocity Pressure ◽  
Pressure Phase

We determine completely the exact Riemann solutions for the system of Euler equations in a duct with discontinuous varying cross-section. The crucial point in solving the Riemann problem for hyperbolic system is the construction of the wave curves. To address the difficulty in the construction due to the nonstrict hyperbolicity of the underlying system, we introduce the L-M and R-M curves in the velocity-pressure phase plane. The behaviors of the L-M and R-M curves for six basic cases are fully analyzed. Furthermore, we observe that in certain cases the L-M and R-M curves contain the bifurcation which leads to the nonuniqueness of the Riemann solutions. Nevertheless, all possible Riemann solutions including classical as well as resonant solutions are solved in a uniform framework for any given initial data.

scholarly journals Singularity Formation for the Compressible Euler Equations

2017 ◽  
Vol 49 (4) ◽  
pp. 2591-2614 ◽  
Author(s):  
Geng Chen ◽  
Ronghua Pan ◽  
Shengguo Zhu
Keyword(s):  
Euler Equations ◽  
Compressible Euler Equations ◽  
Singularity Formation ◽  
Compressible Euler
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