scholarly journals Fluid dynamic limit to the Riemann Solutions of Euler equations: I. Superposition of rarefaction waves and contact discontinuity

2010 ◽  
Vol 3 (4) ◽  
pp. 685-728 ◽  
Author(s):  
Feimin Huang ◽  
◽  
Yi Wang ◽  
Tong Yang ◽  
Keyword(s):  
Euler Equations ◽  
Contact Discontinuity ◽  
Fluid Dynamic ◽  
Rarefaction Waves ◽  
Riemann Solutions ◽  
Fluid Dynamic Limit

Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas

2019 ◽  
Vol 20 (3-4) ◽  
pp. 461-473 ◽  
Author(s):  
Jinhuan Wang ◽  
Yicheng Pang ◽  
Yu Zhang
Keyword(s):  
Euler Equations ◽  
Van Der Waals ◽  
Vacuum State ◽  
Ideal Gas ◽  
Transport Equations ◽  
Rarefaction Waves ◽  
Van Der Waals Gas ◽  
Riemann Solutions ◽  
Riemann Solution ◽  
Isentropic Euler Equations

AbstractIn this paper, we consider limit behaviors of Riemann solutions to the isentropic Euler equations for a non-ideal gas (i.e. van der Waals gas) as the pressure vanishes. Firstly, the Riemann problem of the isentropic Euler equations for van der Waals gas is solved. Then it is proved that, as the pressure vanishes, any Riemann solution containing two shock waves to the isentropic Euler equation for van der Waals gas converges to the delta shock solution to the transport equations and any Riemann solution containing two rarefaction waves tends to the vacuum state solution to the transport equations. Finally, some numerical simulations completely coinciding with the theoretical analysis are demonstrated.

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 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.

Field-line reconnexion in the two-dimensional asymmetric case

1983 ◽  
Vol 30 (2) ◽  
pp. 321-344 ◽  
Author(s):  
V. S. Semenov ◽  
I. V. Kubyshkin ◽  
M. F. Heyn ◽  
H. K. Biernat
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Contact Discontinuity ◽  
Two Dimensional ◽  
Rarefaction Waves ◽  
Plasma Parameters ◽  
Different Types ◽  
Asymmetric Case ◽  
Detailed Mathematical Analysis ◽  
Alfven Velocity

A detailed mathematical analysis of plane steady-state reconnexion is given for the case when the plasma parameters and the magnetic fields are not identical on both sides of the current sheet. Asymptotic solutions in the sense that the inflow velocity is much less than the local Alfvén velocity as well as the arrangement of shock waves are obtained. Rotational (Alfvén) waves, slow shock waves, rarefaction waves (expansion fans), and a contact discontinuity may occur. Four different types of solution, corresponding to different shock wave configurations, are possible. They depend on the parameters of the inflow regions in a unique way.

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.

Kinetic Theory for Bubbly Flow II: Fluid Dynamic Limit

1996 ◽  
Vol 56 (2) ◽  
pp. 358-371 ◽  
Author(s):  
Giovanni Russo ◽  
Peter Smereka
Keyword(s):  
Kinetic Theory ◽  
Fluid Dynamic ◽  
Bubbly Flow ◽  
Fluid Dynamic Limit
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