Relativistic Euler equations for isentropic fluids: Stability of Riemann solutions with large oscillation

2004 ◽  
Vol 55 (6) ◽  
pp. 903-926 ◽  
Author(s):  
Gui-Qiang Chen ◽  
Yachun Li
Keyword(s):  
Euler Equations ◽  
Relativistic Euler Equations ◽  
Riemann Solutions ◽  
Large Oscillation

scholarly journals Riemann problem with delta initial data for the two-dimensional steady pressureless isentropic relativistic Euler equations

2021 ◽  
Author(s):  
Yu Zhang ◽  
Yanyan Zhang
Keyword(s):  
Initial Data ◽  
Euler Equations ◽  
Riemann Problem ◽  
Contact Discontinuity ◽  
Global Solutions ◽  
Two Dimensional ◽  
Relativistic Euler Equations ◽  
Riemann Solutions ◽  
Isentropic Relativistic Euler Equations ◽  
The Stability

The Riemann problem for the two-dimensional steady pressureless isentropic relativistic Euler equations with delta initial data is studied. First, the perturbed Riemann problem with three pieces constant initial data is solved. Then, via discussing the limits of solutions to the perturbed Riemann problem, the global solutions of Riemann problem with delta initial data are completely constructed under the stability theory of weak solutions. Interestingly, the delta contact discontinuity is found in the Riemann solutions of the two-dimensional steady pressureless isentropic relativistic Euler equations with delta initial data.

scholarly journals A new variation for the relativistic Euler equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mahmoud A. E. Abdelrahman ◽  
Hanan A. Alkhidhr
Keyword(s):  
Euler Equations ◽  
Nonlinear Waves ◽  
Approximation Scheme ◽  
Strength Function ◽  
Convergent Sequence ◽  
Approximate Solutions ◽  
Large Initial Data ◽  
Initial Value ◽  
Relativistic Euler Equations ◽  
Glimm Scheme

Abstract The Glimm scheme is one of the so famous techniques for getting solutions of the general initial value problem by building a convergent sequence of approximate solutions. The approximation scheme is based on the solution of the Riemann problem. In this paper, we use a new strength function in order to present a new kind of total variation of a solution. Based on this new variation, we use the Glimm scheme to prove the global existence of weak solutions for the nonlinear ultra-relativistic Euler equations for a class of large initial data that involve the interaction of nonlinear waves.

Second-order accurate kinetic schemes for the ultra-relativistic Euler equations

2003 ◽  
Vol 192 (2) ◽  
pp. 695-726 ◽  
Author(s):  
Matthias Kunik ◽  
Shamsul Qamar ◽  
Gerald Warnecke
Keyword(s):  
Euler Equations ◽  
Second Order ◽  
Relativistic Euler Equations ◽  
Kinetic Schemes

scholarly journals Delta Shocks and Vacuums to the Isentropic Euler Equations with the Flux Perturbation for van der Waals Gas

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jinhuan Wang ◽  
Yongbin Nie ◽  
Samuele De Bartolo
Keyword(s):  
Euler Equations ◽  
Van Der Waals ◽  
Excluded Volume ◽  
Formation Mechanisms ◽  
Van Der Waals Gas ◽  
Riemann Solutions ◽  
Flux Approximation ◽  
Isentropic Euler Equations ◽  
Delta Shocks ◽  
Flux Perturbation

In this paper, we study the isentropic Euler equations with the flux perturbation for van der Waals gas, in which the density has both lower and upper bounds due to the introduction of the flux approximation and the molecular excluded volume. First, we solve the Riemann problem of this system and construct the Riemann solutions. Second, the formation mechanisms of delta shocks and vacuums are analyzed for the Riemann solutions as the pressure, the flux approximation, and the molecular excluded volume all vanish. Finally, some numerical simulations are demonstrated to verify the theoretical analysis.

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