The Riemann problem for an isentropic ideal dusty gas flow with a magnetic field

Pang, Yicheng; Ge, Jianjun; Yang, Huawei; Hu, Mingyou

doi:10.1002/mma.6172

Math Meth Appl Sci

2020

DOI: 10.1002/mma.6172

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The Riemann problem for an isentropic ideal dusty gas flow with a magnetic field

Yicheng Pang

Jianjun Ge

Huawei Yang

et al.

Abstract: This paper deals with Riemann problem for one‐dimensional inviscid, isentropic, and perfectly conducting ideal dusty gas flow with a transverse magnetic field. The explicit expressions of elementary waves are derived in terms of the density, velocity, and transverse magnetic induction of an ideal dusty gas flow. The analytical properties of elementary wave curves and the influence of parameter on the elementary waves are discussed. A new approach is proposed to resolve the Riemann problem. By applying this ap… Show more

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Cited by 3 publications

References 24 publications

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The phenomena of concentration and cavitation in the Riemann solution for the isentropic zero-pressure dusty gasdynamics

Chaturvedi

Singh

2021

Journal of Mathematical Physics

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The aim of the present paper is to investigate the concentration and cavitation phenomenon in the solution of the Riemann problem (RP) to the pressureless isentropic Euler equations for the dusty gas flow by using the two parameter flux approximation. The similar solution of the RP for dusty gas flow is obtained. The formation of δ-shock and vacuum state in the flow field is discussed. Also, it is shown that the solution, containing two shock waves, of the RP to the isentropic Euler equations for dusty gas converges to the δ-shock wave solution of the transport equations and the solution, containing two rarefaction waves, of the RP converges to the vacuum state solution of the transport equations.

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The phenomena of concentration and cavitation in the Riemann solution for the isentropic zero-pressure dusty gasdynamics

Chaturvedi

Singh

2021

Journal of Mathematical Physics

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The transition of Riemann solutions with composite waves for the improved Aw–Rascle–Zhang model in dusty gas

2023

Physics of Fluids

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We study the cavitation and concentration of the Riemann solutions for the improved Aw–Rascle–Zhang (IARZ) model in dusty gas with a non-genuinely nonlinear field. The Riemann solutions containing composite waves are constructed by Liu-entropy condition first. Second, we investigate the limits of the inflection point and tangent point along the 1-family wave curve and find that the composite waves tend to elementary waves as pressure vanishes. Third, we obtain the limiting behavior of the Riemann solutions and observe the formation of δ-shock wave and vacuum as pressure vanishes. We conclude that the limit of Riemann solutions of the IARZ model is not the Riemann solutions of the limit of the IARZ model. The phenomenon is consistent with the work of C. Shen and M. Sun [“Formation of delta-shocks and vacuum states in the vanishing pressure limit of solutions to the Aw–Rascle model,” J. Differ. Equations 249, 3024–3051 (2010)]. Finally, we perform some numerical simulations to verify our theoretical analysis.

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Weak discontinuities in one-dimensional compressible nonideal gas dynamics

Srivastava

Chaturvedi

Singh

2022

Zeitschrift Für Naturforschung A

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This article concerns the study of various parameter effects on the propagation of weak discontinuities by using the method of characteristics. Analytical solutions of the quasi-linear system of hyperbolic partial differential equations (PDEs) are obtained and examined the evolutionary behavior of shock in the characteristic plane. The general behavior of solutions to the Bernoulli equation, which determines the evolution of weak discontinuity in a nonlinear system, is studied in detail. Also, we discuss the formation and distortion of compressive and expansive discontinuities under the van der Waals parameter effect and small particles for planar and cylindrical symmetric flow. The comparison between planar flow and cylindrical symmetric flow is studied under the influence of nonidealness and mass fraction of dust particles. It is found that the compressive waves become shock after a certain lapse of time. The medium considered here is the mixture of van der Waals gas with small dust particles.

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The Riemann problem for an isentropic ideal dusty gas flow with a magnetic field

Cited by 3 publications

References 24 publications

The phenomena of concentration and cavitation in the Riemann solution for the isentropic zero-pressure dusty gasdynamics

The phenomena of concentration and cavitation in the Riemann solution for the isentropic zero-pressure dusty gasdynamics

The transition of Riemann solutions with composite waves for the improved Aw–Rascle–Zhang model in dusty gas

Weak discontinuities in one-dimensional compressible nonideal gas dynamics

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