Effect of the dynamic pressure on the similarity solution of cylindrical shock waves in a rarefied polyatomic gas

• Published in: Ricerche di matematica Vol. 70; no. 1; pp. 195 - 206
• Main Author: Taniguchi, Shigeru
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2021; Springer Nature B.V
• Subjects: Algebra; Analysis; Boundary conditions; Cylindrical waves; Dynamic pressure; Geometry; Group theory; Lie groups; Mathematics; Mathematics and Statistics; Numerical Analysis; Polyatomic gases; Pressure effects; Probability Theory and Stochastic Processes; Relaxation time; Shock waves; Similarity solutions; Spherical waves; Rarefied polyatomic gas; Cylindrical symmetry; 76L05; 35L60; 76N15; 82C35; 76M60; Extended thermodynamics; Similarity solution; Shock wave; Dynamic pressure
• ISSN: 0035-5038; 1827-3491
• DOI: 10.1007/s11587-020-00505-9

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 α 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 α is small. When α 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.