Two-Dimensional Riemann Problems for Chaplygin Gas

Chen, Shuxing; Qu, Aifang

doi:10.1137/110838091

Cited by 55 publications

(30 citation statements)

References 14 publications

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“…Let us also see such as in for the related study on the system (1.1) when

β = 0

. In addition, one can also see for the Riemann problem on the relativistic version of Chaplygin gas equations and for the Riemann problem on the two‐dimensional Chaplygin gas equations.…”

Section: Introductionmentioning

confidence: 97%

The Riemann problem for the Chaplygin gas equations with a source term

Shen

2015

Z Angew Math Mech

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Key words Chaplygin gas equations, Riemann problem, delta shock wave, Coulomb-like friction term. MSC (2010) 35L65, 35L67, 35B30, 76N10The Riemann solutions for the one-dimensional Chaplygin gas equations with a Coulomb-like friction term are constructed explicitly. It is shown that the delta shock wave appears in the Riemann solutions in some certain situations. The generalized Rankine-Hugoniot conditions of delta shock wave are established and the position, propagation speed and strength of delta shock wave are given, which enables us to see the influence of Coulomb-like friction term on the Riemann solutions for the Chaplygin gas equations clearly. In addition, the relations connected with the area transportation are derived which include mass and momentum transportation.

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“…Let us also see such as in for the related study on the system (1.1) when

β = 0

. In addition, one can also see for the Riemann problem on the relativistic version of Chaplygin gas equations and for the Riemann problem on the two‐dimensional Chaplygin gas equations.…”

Section: Introductionmentioning

confidence: 97%

The Riemann problem for the Chaplygin gas equations with a source term

Shen

2015

Z Angew Math Mech

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“…In contrast to the traditional isentropic Chaplygin gas dynamic system, the solution to the Riemann problem (1.3) and (1.4) is either the combination of three contact discontinuities when u − − 1 ρ − < u + + 1 ρ + or the delta shock wave solution when u − − 1 ρ − > u + + 1 ρ + , which can be obtained by using more complicated generalized Rankine-Hugoniot conditions. It is clear to see that the wave interaction problem for the system (1.3) studied here is more complicated than that in [13] for the traditional isentropic Chaplygin gas dynamic system, which is the building block to construct the solutions to the two-dimensional Riemann problem [6,12,18,19,31,45] for the isentropic Chaplygin gas system (1.1) with the equation of state p(ρ) = − 1 ρ . The plan of the paper is displayed in the following way.…”

Section: Introductionmentioning

confidence: 99%

On the delta shockwave interactions for the isentropic Chaplygin gas system consisting of three scalar equations

Sun

Xin

2019

Filomat

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The Riemann problem for the one-dimensional version of isentropic compressible Euler system for the Chaplygin gas consisting of three scalar equations is considered. It is shown that the Riemann solutions involve only two situations: the combination of three contact discontinuities or a delta shock wave. The generalized Rankine-Hugoniot conditions of delta shock wave are derived and the exact delta shock wave solution including the strength and propagation speed is obtained explicitly. The solutions to the perturbed Riemann problem are constructed globally when the initial data are taken to be the three piecewise constant initial data. The wave interaction problem is extensively investigated and some interesting phenomena are observed. It is shown that the limits of solutions to the perturbed Riemann problem converge to the corresponding ones to the Riemann problem when the perturbation parameter tends to zero. (Jie Xin) J 1 (ρ 3 , u 3 , v + ) J 7 0 J 9 0 J 10 0 J 8 0 J 6 0 J 8 0 J 5 0 J 7 0 J 2 0 J 3 0 J 4

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“…For the Riemann problem of homogeneous Chaplygin gas equations, there are lots of results. We refer the readers to [17][18][19][20][21][22][23]. For inhomogeneous Chaplygin gas equations, Shen [24] studied Riemann problem by introducing a new velocity:…”

Section: Introductionmentioning

confidence: 99%

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

Fan

Guo

Yin

2018

Advances in Mathematical Physics

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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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Two-Dimensional Riemann Problems for Chaplygin Gas

Cited by 55 publications

References 14 publications

The Riemann problem for the Chaplygin gas equations with a source term

The Riemann problem for the Chaplygin gas equations with a source term

On the delta shockwave interactions for the isentropic Chaplygin gas system consisting of three scalar equations

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

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