Non-relativistic limits of rarefaction wave to the 1-D piston problem for the isentropic relativistic Euler equations

2017 ◽  
Vol 58 (8) ◽  
pp. 081510 ◽  
Author(s):  
Min Ding ◽  
Yachun Li
Keyword(s):  
Rarefaction Wave ◽  
Euler Equations ◽  
Piston Problem ◽  
Relativistic Euler Equations ◽  
Isentropic Relativistic Euler Equations

Riemann problem and limits of solutions to the isentropic relativistic Euler equations for isothermal gas with flux approximation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yu Zhang ◽  
Yanyan Zhang
Keyword(s):  
Shock Wave ◽  
Euler Equations ◽  
Riemann Problem ◽  
Delta Shock Wave ◽  
Relativistic Euler Equations ◽  
Delta Shock ◽  
Isentropic Relativistic Euler Equations ◽  
Flux Approximation ◽  
Two Parameter ◽  
Pressureless Relativistic Euler Equations

Abstract We are concerned with the vanishing flux-approximation limits of solutions to the isentropic relativistic Euler equations governing isothermal perfect fluid flows. The Riemann problem with a two-parameter flux approximation including pressure term is first solved. Then, we study the limits of solutions when the pressure and two-parameter flux approximation vanish, respectively. It is shown that, any two-shock-wave Riemann solution converges to a delta-shock solution of the pressureless relativistic Euler equations, and the intermediate density between these two shocks tends to a weighted δ-measure that forms a delta shock wave. By contract, any two-rarefaction-wave solution tends to a two-contact-discontinuity solution of the pressureless relativistic Euler equations, and the intermediate state in between tends to a vacuum state.

Global solution to a three-dimensional spherical piston problem for the relativistic Euler equations

2020 ◽  
pp. 1-26
Author(s):  
LAI GENG
Keyword(s):  
Euler Equations ◽  
Wave Motion ◽  
Surrounding Medium ◽  
Three Dimensional ◽  
Spherically Symmetric ◽  
Piston Problem ◽  
Relativistic Euler Equations ◽  
Symmetric Motion ◽  
Characteristics Method ◽  
Spherically Symmetric Motion

The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we consider a ‘spherical piston’ problem for the relativistic Euler equations, which describes the wave motion produced by a sphere expanding into an infinite surrounding medium. We use the reflected characteristics method to construct a global piecewise smooth solution with a single shock of this spherical piston problem, provided that the speed of the sphere is a small perturbation of a constant speed.

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