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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Angheluta-Bauer, Luiza / Chen, Xi / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi / Yang, Xu


IMPACT FACTOR 2018: 1.033
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2191-0294
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Volume 20, Issue 3-4

Issues

Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas

Jinhuan Wang
  • Corresponding author
  • Department of Mathematics and Information Science, Tangshan Normal University, Tangshan 063000, PR China
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/ Yicheng Pang / Yu Zhang
Published Online: 2019-03-19 | DOI: https://doi.org/10.1515/ijnsns-2018-0263

Abstract

In this paper, we consider limit behaviors of Riemann solutions to the isentropic Euler equations for a non-ideal gas (i.e. van der Waals gas) as the pressure vanishes. Firstly, the Riemann problem of the isentropic Euler equations for van der Waals gas is solved. Then it is proved that, as the pressure vanishes, any Riemann solution containing two shock waves to the isentropic Euler equation for van der Waals gas converges to the delta shock solution to the transport equations and any Riemann solution containing two rarefaction waves tends to the vacuum state solution to the transport equations. Finally, some numerical simulations completely coinciding with the theoretical analysis are demonstrated.

Keywords: Isentropic Euler equations; Van der Waals gas; delta shock wave; vacuum state; vanishing pressurelimit; transport equations

PACS: 35L65; 35L45

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About the article

Received: 2018-09-03

Accepted: 2019-02-20

Published Online: 2019-03-19

Published in Print: 2019-05-26


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 20, Issue 3-4, Pages 461–473, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2018-0263.

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