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Reduced kinetic model of polyatomic gases

Published online by Cambridge University Press:  12 May 2023

Praveen Kumar Kolluru Open the ORCID record for Praveen Kumar Kolluru [Opens in a new window] ,
Mohammad Atif Open the ORCID record for Mohammad Atif [Opens in a new window]  and
Santosh Ansumali Open the ORCID record for Santosh Ansumali [Opens in a new window]
Praveen Kumar Kolluru
Affiliation:
Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
Mohammad Atif
Affiliation:
Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
Santosh Ansumali*
Affiliation:
Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
*
†Email address for correspondence: ansumali@jncasr.ac.in
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Abstract

Kinetic models of polyatomic gas typically account for the internal degrees of freedom at the level of the two-particle distribution function. However, close to the hydrodynamic limit, the internal (rotational) degrees of freedom tend to be well represented just by rotational kinetic energy density. We account for the rotational energy by augmenting the ellipsoidal statistical Bhatnagar–Gross–Krook (ES–BGK) model, an extension of the BGK model, at the level of the single-particle distribution function with an advection–diffusion–relaxation equation for the rotational energy. This reduced model respects the $H$ theorem and recovers the compressible hydrodynamics for polyatomic gases as its macroscopic limit. As required for a polyatomic gas model, this extension of the ES–BGK model not only has the correct specific heat ratio but also allows for three independent tunable transport coefficients: thermal conductivity, shear viscosity and bulk viscosity. We illustrate the effectiveness of the model via a lattice Boltzmann method implementation.

JFM classification

Rarefied Gas Flow: Kinetic theory Mathematical Foundations: Computational methods Mathematical Foundations: General fluid mechanics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 963 , 25 May 2023 , A7
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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