Delta shock wave to the compressible fluid flow with the generalized Chaplygin gas

Pang, Yicheng; Zhang, Yu; Wen, Yongsong

doi:10.1016/j.ijnonlinmec.2017.12.014

Cited by 14 publications

(3 citation statements)

References 27 publications

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“…Lu [7] and Cheng [8] proved analytically an existence theorem for the global entropy solutions in the case of γ > 3 and 1 < γ < 3 respectively, by means of the theory of compensated compactness coupled with some basic ideas of kinetic formulation. For the negative pressure laws, Cheng et al [9] studied the Riemann problem for the 1D compressible fluid flow of a Chaplygin gas and solved constructively the existence and uniqueness of delta shock solutions, and the model of generalized Chaplygin gas was also investigated by Pang et al [10].…”

Section: Introductionmentioning

confidence: 99%

Measure solutions to piston problem for compressible fluid flow of generalized chaplygin gas

Huang¹,

Wang²,

Shao³

2022

Preprint

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We study the piston problem of the compressible fluid flow with the generalized Chaplygin gas. Depending on the inferential critical value of Mach number, we prove that, there exists an integral weak solution for the proceeding piston problem, consisting of a shock separating constant states ahead of the piston if Mach numbers less than this critical value, while a singular measure solution, with density containing a Dirac measure supported on the piston, shall be proposed to solve the proceeding piston problem if Mach numbers greater than or equal to the critical value. For the receding piston problem, rarefaction wave solution always exists when the piston recedes from the gas with any constant speed. Moreover, the occurrence of vacuum state and the convergence of solutions, as well as degeneration of equations are analyzed in the receding case as Mach number tends to infinity.

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Section: Introductionmentioning

confidence: 99%

Measure solutions to piston problem for compressible fluid flow of generalized chaplygin gas

Huang¹,

Wang²,

Shao³

2022

Preprint

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“…The complete solution of the Riemann Problem associated with a compressible flow of the generalized Chaplygin gas was presented by Pang et al [13], accounting for a delta shock wave. Abbassi and Namah [14] describe the oil-water interface of the displacement of oil by water injection in a porous medium (representing an oil reservoir).…”

Section: Introductionmentioning

confidence: 99%

A New Constitutive Relation for Describing the Flow through Porous Media with Unsaturated–Saturated Transition

Martins‐Costa

Silva

et al. 2019

Mathematical Problems in Engineering

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The present work proposes an adequate constitutive relation to treat the process of filling with a fluid porous medium. This relation assures the problem to remain hyperbolic when the porous medium is saturated by the fluid. When the fluid fraction reaches porosity, the proposed constitutive relation increases the porous matrix resistance to more fluid inlet due to an important feature: it is a continuous and differentiable function with first derivative being also an increasing function. This allows assuring that the fluid fraction may exceed the porosity only by a very small value, making the constitutive relation realistic. Some examples compare this new constitutive relation with previous ones, highlighting its advantages.

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“…Recently, the Riemann problem for the Euler equations of compressible fluid flow with the generalized Chaplygin gas was studied by Pang et al [17].…”

Section: Introductionmentioning

confidence: 99%

Concentration of mass in the pressureless limit of the Euler equations of one-dimensional compressible fluid flow

Sheng

Shao

2019

Preprint

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Delta shock wave to the compressible fluid flow with the generalized Chaplygin gas

Cited by 14 publications

References 27 publications

Measure solutions to piston problem for compressible fluid flow of generalized chaplygin gas

Measure solutions to piston problem for compressible fluid flow of generalized chaplygin gas

A New Constitutive Relation for Describing the Flow through Porous Media with Unsaturated–Saturated Transition

Concentration of mass in the pressureless limit of the Euler equations of one-dimensional compressible fluid flow

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