The Riemann problem for the relativistic full Euler system with generalized Chaplygin proper energy density–pressure relation

2018 ◽  
Vol 69 (2) ◽  
Author(s):  
Zhiqiang Shao
Keyword(s):  
Energy Density ◽  
Riemann Problem ◽  
Euler System ◽  
Proper Energy

Generalised Riemann problem for Euler system

2017 ◽  
Vol 60 (4) ◽  
pp. 581-592
Author(s):  
ShuXing Chen ◽  
DeNing Li
Keyword(s):  
Riemann Problem ◽  
Euler System ◽  
Generalised Riemann Problem

THE RIEMANN PROBLEM FOR THE MULTI-PRESSURE EULER SYSTEM

2005 ◽  
Vol 02 (03) ◽  
pp. 745-782 ◽  
Author(s):  
C. CHALONS ◽  
F. COQUEL
Keyword(s):  
Riemann Problem ◽  
Stokes Equations ◽  
Traveling Wave Solutions ◽  
Viscosity Coefficient ◽  
Continuous Functions ◽  
Euler System ◽  
Small Scale ◽  
Riemann Solutions ◽  
Lipschitz Continuous ◽  
Kinetic Relations

We prove the existence and uniqueness of the Riemann solutions to the Euler equations closed by N independent constitutive pressure laws. This model stands as a natural asymptotic system for the multi-pressure Navier–Stokes equations in the regime of infinite Reynolds number. Due to the inherent lack of conservation form in the viscous regularization, the limit system exhibits measure-valued source terms concentrated on shock discontinuities. These non-positive bounded measures, called kinetic relations, are known to provide a suitable tool to encode the small-scale sensitivity in the singular limit. Considering N independent polytropic pressure laws, we show that these kinetic relations can be derived by solving a simple algebraic problem which governs the endpoints of the underlying viscous shock profiles, for any given but prescribed ratio of viscosity coefficient in the viscous perturbation. The analysis based on traveling wave solutions allows us to introduce the asymptotic Euler system in the setting of piecewise Lipschitz continuous functions and to study the Riemann problem.

scholarly journals Uniqueness of rarefaction waves in multidimensional compressible Euler system

2015 ◽  
Vol 12 (03) ◽  
pp. 489-499 ◽  
Author(s):  
Eduard Feireisl ◽  
Ondřej Kreml
Keyword(s):  
Shock Wave ◽  
Rarefaction Wave ◽  
Riemann Problem ◽  
Euler System ◽  
Entropy Solutions ◽  
Infinitely Many Solutions ◽  
Rarefaction Waves ◽  
Convex Integration ◽  
Wave Solutions ◽  
Compressible Euler

We show that 1D rarefaction wave solutions are unique in the class of bounded entropy solutions to the multidimensional compressible Euler system. Such a result may be viewed as a counterpart of the recent examples of non-uniqueness of the shock wave solutions to the Riemann problem, where infinitely many solutions are constructed by the method of convex integration.

scholarly journals On two-dimensional Riemann problem for pressure-gradient equations of the Euler system

1998 ◽  
Vol 4 (4) ◽  
pp. 609-634 ◽  
Author(s):  
Peng Zhang ◽  
◽  
Jiequan Li ◽  
Tong Zhang ◽  
◽  
...  
Keyword(s):  
Pressure Gradient ◽  
Riemann Problem ◽  
Euler System ◽  
Two Dimensional ◽  
Pressure Gradient Equations

scholarly journals Nakedly singular counterpart of Schwarzschild’s incompressible star. A barotropic continuity condition in the center

2019 ◽  
Vol 51 (11) ◽  
Author(s):  
Łukasz Bratek ◽  
Joanna Jałocha ◽  
Andrzej Woszczyna
Keyword(s):  
Energy Density ◽  
Incompressible Fluid ◽  
Equations Of State ◽  
Continuity Condition ◽  
Interior Solution ◽  
Regularity Conditions ◽  
Initial Condition ◽  
Static Sphere ◽  
Proper Energy

Abstract A static sphere of incompressible fluid with uniform proper energy density is considered as an example of exact star-like solution with weakened central regularity conditions characteristic of a nakedly singular spherical vaccuum solution. The solution is a singular counterpart of the Schwarzschild’s interior solution. The initial condition in the center for general barotropic equations of state is established.

scholarly journals Nonuniqueness of Admissible Weak Solution to the Riemann Problem for the Full Euler System in Two Dimensions

2020 ◽  
Vol 52 (2) ◽  
pp. 1729-1760 ◽  
Author(s):  
Hind Al Baba ◽  
Christian Klingenberg ◽  
Ondřej Kreml ◽  
Václav Mácha ◽  
Simon Markfelder
Keyword(s):  
Weak Solution ◽  
Riemann Problem ◽  
Euler System ◽  
Two Dimensions

scholarly journals Computational experiments with the AUSM technique

2021 ◽  
pp. 1-28
Author(s):  
Viktor Vasilievich Val'ko ◽  
Nikita Olegovych Savenko ◽  
Anton Alekseevich Bay
Keyword(s):  
Riemann Problem ◽  
Unstructured Grids ◽  
Splitting Method ◽  
Three Dimensional ◽  
Euler System ◽  
Splitting Methods ◽  
Computational Experiments ◽  
Stagnation Zone ◽  
One Dimensional ◽  
Flow Splitting

In this paper, we discuss computational experiments based on the “AUSM” stream splitting methods. The efficiency of using various pressure approximations for flow splitting according to the original AUSM method is shown. The proposed use of splitting is tested on one-dimensional and three-dimensional problems. Partial use of the flow splitting method, only in terms of pressure, is proposed to be used in the calculations of the Euler system on unstructured grids. A variant of the application of the method of strong deceleration of the flow in the calculations of the flow around obtuse bodies is considered. The algorithm of the method for calculating flows with an extended stagnation zone, within which the Mach numbers decrease to about ~ 0.1, is investigated. Comparison with high-precision methods based on the solution of the Riemann problem is given.

scholarly journals Solutions with concentration and cavitation to the Riemann problem for the isentropic relativistic Euler system for the extended Chaplygin gas

2019 ◽  
Vol 17 (1) ◽  
pp. 220-241 ◽  
Author(s):  
Yunfeng Zhang ◽  
Meina Sun ◽  
Xiuli Lin
Keyword(s):  
Riemann Problem ◽  
Vacuum State ◽  
Chaplygin Gas ◽  
Euler System ◽  
Phase Plane Analysis ◽  
Delta Shock Wave ◽  
Plane Analysis ◽  
Delta Shock ◽  
Riemann Solution ◽  
Shock Wave Solution

Abstract The solutions to the Riemann problem for the isentropic relativistic Euler system for the extended Chaplygin gas are constructed for all kinds of situations by using the method of phase plane analysis. The asymptotic limits of solutions to the Riemann problem for the relativistic extended Chaplygin Euler system are investigated in detail when the pressure given by the equation of state of extended Chaplygin gas becomes that of the pressureless gas. During the process of vanishing pressure, the phenomenon of concentration can be identified and analyzed when the two-shock Riemann solution tends to a delta shock wave solution as well as the phenomenon of cavitation also being captured and observed when the two-rarefaction-wave Riemann solution tends to a two-contact-discontinuity solution with a vacuum state between them.

Sign in / Sign up

Export Citation Format

Share Document