Behavior of Riemann Solutions of Extended Chaplygin Gas Under the Limiting Condition

2021 ◽  
Vol 174 (1) ◽  
Author(s):  
Yating Song ◽  
Lihui Guo
Keyword(s):  
Chaplygin Gas ◽  
Riemann Solutions ◽  
Limiting Condition

scholarly journals The Vanishing Pressure Limit of Riemann Solutions to the Non-Isentropic Euler Equations for Generalized Chaplygin Gas

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Qixia Ding ◽  
Lihui Guo
Keyword(s):  
Shock Wave ◽  
Contact Discontinuity ◽  
Vacuum State ◽  
Chaplygin Gas ◽  
Delta Shock Wave ◽  
Generalized Chaplygin Gas ◽  
Riemann Solutions ◽  
Pressure Limit ◽  
Delta Shock ◽  
Riemann Solution

We analyze the appearance of delta shock wave and vacuum state in the vanishing pressure limit of Riemann solutions to the non-isentropic generalized Chaplygin gas equations. As the pressure vanishes, the Riemann solution including two shock waves and possible one contact discontinuity converges to a delta shock wave solution. Both the densityρand the internal energyHsimultaneously present a Dirac delta singularity. And the Riemann solution involving two rarefaction waves and possible one contact discontinuity converges to a solution involving vacuum state of the transport equations.

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