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

  • Jinhuan Wang EMAIL logo , Yicheng Pang and Yu Zhang
Published/Copyright: March 19, 2019

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.

PACS: 35L65; 35L45

Acknowledgements

This work is supported by the Science and Technology Foundation of Hebei Education Department (QN2018307) and the Doctor Foundation of Tangshan Normal University (2015A07).

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Received: 2018-09-03
Accepted: 2019-02-20
Published Online: 2019-03-19
Published in Print: 2019-05-26

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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