The similarity solution for a strong cylindrical shock wave in a rarefied polyatomic gas is analyzed on the basis of Rational Extended Thermodynamics with six independent fields; the mass density, the velocity, the pressure and the dynamic pressure. A new ODE system for the similarity solution is derived in a systematic way by using the method based on the Lie group theory proposed in the context of the spherical shock wave in a rarefied monoatomic gas in Donato and Ruggeri (J Math Anal Appl 251:395, 2000). The boundary conditions are also specified from the Rankine–Hugoniot conditions for the sub-shock. The derived similarity solution is characterized by only one dimensionless parameter \(\alpha \) related to the relaxation time for the dynamic pressure. The numerical analysis of the similarity solution is also performed. The solution agrees with the well-known Sedov–von Neumann–Taylor (SNT) solution when \(\alpha \) is small. When \(\alpha \) is larger, due to the presence of the dynamic pressure, the deviation from the SNT solution is evident; the strength of a peak near the shock front becomes smaller and the profile becomes broader.
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The present paper is dedicated to Professor Masaru Sugiyama who invited the author to the present research field and always encourages him to proceed with the study. The author thanks Professor Tommaso Ruggeri for valuable discussions. The results contained in the present paper have been partially presented in WASCOM 2019. This work was supported by JSPS KAKENHI Grant Number JP19K04204.
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Taniguchi, S. Effect of the dynamic pressure on the similarity solution of cylindrical shock waves in a rarefied polyatomic gas. Ricerche mat (2020). https://doi.org/10.1007/s11587-020-00505-9
- Shock wave
- Extended thermodynamics
- Similarity solution
- Cylindrical symmetry
- Rarefied polyatomic gas
- Dynamic pressure
Mathematics Subject Classification