The limiting behavior of the Riemann solutions of non-isentropic modified Chaplygin gas dynamics

2021 ◽  
Vol 62 (4) ◽  
pp. 041501
Author(s):  
Weifeng Jiang ◽  
Tong Li ◽  
Zhen Wang ◽  
Shutian Fang
Keyword(s):  
Gas Dynamics ◽  
Chaplygin Gas ◽  
Modified Chaplygin Gas ◽  
Riemann Solutions ◽  
Limiting Behavior

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.

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 Dynamical system analysis of FLRW models with Modified Chaplygin gas

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ali Osman Yılmaz ◽  
Ertan Güdekli
Keyword(s):  
Dynamical System ◽  
Equation Of State ◽  
Energy Density ◽  
System Analysis ◽  
Chaplygin Gas ◽  
Modified Chaplygin Gas ◽  
State Spaces ◽  
The Universe ◽  
Matter Energy ◽  
Far Future

AbstractWe investigate Friedmann–Lamaitre–Robertson–Walker (FLRW) models with modified Chaplygin gas and cosmological constant, using dynamical system methods. We assume $$p=(\gamma -1)\mu -\dfrac{A}{\mu ^\alpha }$$ p = ( γ - 1 ) μ - A μ α as equation of state where $$\mu$$ μ is the matter-energy density, p is the pressure, $$\alpha$$ α is a parameter which can take on values $$0<\alpha \le 1$$ 0 < α ≤ 1 as well as A and $$\gamma$$ γ are positive constants. We draw the state spaces and analyze the nature of the singularity at the beginning, as well as the fate of the universe in the far future. In particular, we address the question whether there is a solution which is stable for all the cases.

scholarly journals Reduced modified Chaplygin gas cosmology

2015 ◽  
Vol 2015 (2) ◽  
Author(s):  
Jianbo Lu ◽  
Danhua Geng ◽  
Lixin Xu ◽  
Yabo Wu ◽  
Molin Liu
Keyword(s):  
Chaplygin Gas ◽  
Modified Chaplygin Gas
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