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Article

Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats

by
Shingo Kosuge
1 and
Kazuo Aoki
2,*
1
Institute for Liberal Arts and Sciences, Kyoto University, Kyoto 606-8501, Japan
2
Department of Mathematics, National Cheng Kung University, Tainan 70101, Taiwan
*
Author to whom correspondence should be addressed.
Fluids 2023, 8(1), 5; https://doi.org/10.3390/fluids8010005
Submission received: 11 November 2022 / Revised: 10 December 2022 / Accepted: 16 December 2022 / Published: 22 December 2022
(This article belongs to the Special Issue Bulk Viscosity and Relaxation Processes: Revisited)
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Abstract

A system of Navier–Stokes-type equations with two temperatures is derived, for a polyatomic gas with temperature-dependent specific heats (thermally perfect gas), from the ellipsoidal statistical (ES) model of the Boltzmann equation extended to such a gas. Subsequently, the system is applied to the problem of shock-wave structure for a gas with large bulk viscosity (or, equivalently, with slow relaxation of the internal modes), and the numerical results are compared with those based on the ordinary Navier–Stokes equations. It is shown that the latter equations fail to describe the double-layer structure of shock profiles for a gas with large bulk viscosity.
Keywords: polyatomic gases; bulk viscosity; Navier–Stokes equations; ES model; shock-wave structure; thermally perfect gases polyatomic gases; bulk viscosity; Navier–Stokes equations; ES model; shock-wave structure; thermally perfect gases

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MDPI and ACS Style

Kosuge, S.; Aoki, K. Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats. Fluids 2023, 8, 5. https://doi.org/10.3390/fluids8010005

AMA Style

Kosuge S, Aoki K. Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats. Fluids. 2023; 8(1):5. https://doi.org/10.3390/fluids8010005

Chicago/Turabian Style

Kosuge, Shingo, and Kazuo Aoki. 2023. "Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats" Fluids 8, no. 1: 5. https://doi.org/10.3390/fluids8010005

APA Style

Kosuge, S., & Aoki, K. (2023). Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats. Fluids, 8(1), 5. https://doi.org/10.3390/fluids8010005

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