scholarly journals The Perturbed Riemann Problem for the Aw-Rascle Model with Modified Chaplygin Gas Pressure

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yujin Liu ◽  
Wenhua Sun
Keyword(s):  
Riemann Problem ◽  
Large Time ◽  
Chaplygin Gas ◽  
Global Structure ◽  
Gas Pressure ◽  
Modified Chaplygin Gas ◽  
Riemann Solutions ◽  
Asymptotic Behaviors ◽  
Piecewise Constant ◽  
The Stability

This paper is concerned with the perturbed Riemann problem for the Aw-Rascle model with the modified Chaplygin gas pressure. We obtain constructively the solutions when the initial values are three piecewise constant states. The global structure and the large-time asymptotic behaviors of the solutions are discussed case by case. Further, we obtain the stability of the corresponding Riemann solutions as the initial perturbed parameter tends to zero.

scholarly journals On a Nonsymmetric Keyfitz-Kranzer System of Conservation Laws with Generalized and Modified Chaplygin Gas Pressure Law

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Hongjun Cheng ◽  
Hanchun Yang
Keyword(s):  
Shock Wave ◽  
Conservation Laws ◽  
Chaplygin Gas ◽  
Gas Pressure ◽  
Modified Chaplygin Gas ◽  
Delta Shock Wave ◽  
Generalized Chaplygin Gas ◽  
Riemann Solutions ◽  
Delta Shock ◽  
System Of Conservation Laws

This paper is devoted to the study of a nonsymmetric Keyfitz-Kranzer system of conservation laws with the generalized and modified Chaplygin gas pressure law, which may admit delta shock waves, a topic of interest. Firstly, we solve the Riemann problems with piecewise constant data having a single discontinuity. For the generalized Chaplygin gas pressure law, the solution consists of three different structures:R+J,S+J, andδ. Existence and uniqueness of delta shock solution are established under the generalized Rankine-Hugoniot relation and entropy condition. For the modified Chaplygin gas pressure law, the structures of solution areR+JandS+J. Secondly, we discuss the limits of Riemann solutions for the modified Chaplygin gas pressure law as the pressure law tends to the generalized Chaplygin gas one. In particular, for some cases, the solutionS+Jtends to a delta shock wave, and it is different from the delta shock wave for the generalized Chaplygin gas pressure law with the same initial data. Thirdly, we simulate the Riemann solutions and examine the formation process of delta shock wave by employing the Nessyahu-Tadmor scheme. The numerical results are coincident with the theoretical analysis.

scholarly journals Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Pengpeng Ji ◽  
Chun Shen
Keyword(s):  
Initial Data ◽  
Riemann Problem ◽  
Phase Plane ◽  
Wave Interaction ◽  
Global Solutions ◽  
Geometrical Structures ◽  
Small Perturbations ◽  
Riemann Solutions ◽  
Piecewise Constant ◽  
Rarefaction Curves

The global solutions of the perturbed Riemann problem for the Leroux system are constructed explicitly under the suitable assumptions when the initial data are taken to be three piecewise constant states. The wave interaction problems are widely investigated during the process of constructing global solutions with the help of the geometrical structures of the shock and rarefaction curves in the phase plane. In addition, it is shown that the Riemann solutions are stable with respect to the specific small perturbations of the Riemann initial data.

scholarly journals Spherical "Top-Hat" collapse in a modified Chaplygin gas dominated universe

2015 ◽  
Vol 24 (07) ◽  
pp. 1550050 ◽  
Author(s):  
S. Karbasi ◽  
H. Razmi
Keyword(s):  
Equation Of State ◽  
Structure Formation ◽  
Observational Data ◽  
Chaplygin Gas ◽  
Modified Chaplygin Gas ◽  
Time Rate ◽  
Generalized Chaplygin Gas ◽  
The Stability ◽  
Perturbation Growth ◽  
Good Agreement

Considering perturbation growth in spherical Top-Hat (STH) model of structure formation in a generalized Chaplygin gas (GCG) dominated universe, we want to study this scenario with modified Chaplygin gas (MCG) obeying an equation of state p = A - B/ρα model. Different parameters of this scenario for positive and negative values of A are computed. The evolution of background and collapsed region parameters are found for different cases. The stability of the model and the collapse time rate are considered in different cases. The turn-around redshifts for different values of α are computed; the results are in relatively good agreement with current observational data.

scholarly journals Stability and interacting f(T, T ) gravity with modified Chaplygin gas

2017 ◽  
Vol 95 (11) ◽  
pp. 1068-1073 ◽  
Author(s):  
T. Mirzaei Rezaei ◽  
Alireza Amani
Keyword(s):  
Dark Energy ◽  
Cosmological Parameters ◽  
Teleparallel Gravity ◽  
Chaplygin Gas ◽  
Accelerated Expansion ◽  
Phase Plane Analysis ◽  
Modified Chaplygin Gas ◽  
Continuity Equations ◽  
The Stability ◽  
The Universe

In this paper, the model of interaction is studied between f(T, [Formula: see text]) gravity and modified Chaplygin gas in Friedmann–Robertson–Walker (FRW)-flat metric. We obtain the Friedmann equations in the framework of teleparallel gravity by vierbein field. We consider that the Universe is dominated by components of cold matter, dark energy, and modified Chaplygin gas. In what follows we separately write the corresponding continuity equations for components of the Universe. Also, dark energy equation of state (EoS) and effective EoS are obtained with respect to redshift, thereinafter the corresponding cosmological parameters are plotted in terms of redshift, thereinafter the accelerated expansion of the Universe is investigated. Finally, the stability of the model is discussed in phase plane analysis.

scholarly journals Analysis of the Stability of the Riemann Problem for a Simplified Model in Magnetogasdynamics

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yujin Liu ◽  
Wenhua Sun
Keyword(s):  
Shock Wave ◽  
Riemann Problem ◽  
Contact Discontinuity ◽  
Ideal Gas ◽  
Simplified Model ◽  
Characteristic Method ◽  
Small Perturbations ◽  
Riemann Solutions ◽  
One Dimensional ◽  
The Stability

The generalized Riemann problem for a simplified model of one-dimensional ideal gas in magnetogasdynamics in a neighborhood of the origin(t>0)in the(x,t)plane is considered. According to the different cases of the corresponding Riemann solutions, we construct the perturbed solutions uniquely with the characteristic method. We find that, for some case, the contact discontinuity appears after perturbation while there is no contact discontinuity of the corresponding Riemann solution. For most cases, the Riemann solutions are stable and the perturbation can not affect the corresponding Riemann solutions. While, for some few cases, the forward (backward) rarefaction wave can be transformed into the forward (backward) shock wave which shows that the Riemann solutions are unstable under such local small perturbations of the Riemann initial data.

scholarly journals The Convergence of Riemann Solutions to the Modified Chaplygin Gas Equations with a Coulomb-Like Friction Term as the Pressure Vanishes

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Yongqiang Fan ◽  
Lihui Guo ◽  
Gan Yin
Keyword(s):  
Source Term ◽  
Chaplygin Gas ◽  
Euler System ◽  
Modified Chaplygin Gas ◽  
Riemann Solutions ◽  
Delta Shock ◽  
Vacuum States ◽  
Friction Term ◽  
Self Similar ◽  
Delta Shock Waves

This paper studies the convergence of Riemann solutions to the inhomogeneous modified Chaplygin gas equations as the pressure vanishes. The delta shock waves and vacuum states occur as the pressure vanishes. The Riemann solutions of inhomogeneous modified Chaplygin gas equations are no longer self-similar. It is obviously different from the Riemann solutions of homogeneous modified Chaplygin gas equations. When the pressure vanishes, the Riemann solutions of the modified Chaplygin gas equations with a coulomb-like friction term converge to the Riemann solutions of the pressureless Euler system with a source term.

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