https://doi.org/10.1140/epjp/s13360-025-06073-x
Regular Article
Improved theory for shock waves using simplified van der Waals equation of state at high Mach numbers
1
College of Science, Inner Mongolia University of Technology, Inner Mongolia, 010051, Hohhot, China
2
School of Civil Engineering and Water Resources, Qinghai University, 810016, Qinghai, Xining, China
a
2238033845@qq.com
b
jiyongchao110@126.com
Received:
9
August
2024
Accepted:
2
February
2025
Published online:
4
March
2025
The primary goal of this research is to present an improved shock wave theory that takes into account the gaseous non-ideality for a monatomic gas system composed of hard-sphere molecules using simplified van der Waals equation of state at high Mach numbers. In non-ideal gas, dimensionless conservation equations and new Rankine–Hugoniot conditions are given. The SSTNM (similar simplified translational non-equilibrium model) and OBurnett constitutive equations with non-ideal parameters are extended. The differential equations of improved theory for shock waves are established and solved. The validity of constitutive relations in non-ideal gas situations is proved, and the results are verified by direct simulation Monte Carlo methods. By examining the orbital structure, internal structure of shock waves and structural parameters of density–temperature separation, it becomes apparent that the improved shock wave theory considering the gaseous non-ideality has a better predictive effect than treating it as an ideal gas. Further experimental verification using density results indicates that the higher the Mach number, the closer the results predicted by the two constitutive equations are to the experimental results in the prediction region they are good at. This article improves the prediction effect of the shock wave structure using the improved shock wave theory, and it also introduces novel perspectives and strategies for avoiding the use of high-order constitutive relations that are prone to numerical instability.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
