Derivation and numerical comparison of Shakhov and Ellipsoidal Statistical kinetic models for a monoatomic gas mixture

Todorova, B. N. and Steijl, R. (2019) Derivation and numerical comparison of Shakhov and Ellipsoidal Statistical kinetic models for a monoatomic gas mixture. European Journal of Mechanics - B/Fluids, 76, pp. 390-402. (doi: 10.1016/j.euromechflu.2019.04.001)

Abstract

Gas mixtures are important for many practical applications. Extending kinetic model equations of the Bhatnagar–Gross–Krook (BGK) type from a single-species gas to a multi-species gas mixture presents a number of significant challenges. First, obtaining the correct species diffusions, viscous stresses as well as heat conduction in the continuum limit requires a careful design of the collision terms in the kinetic equations. Secondly, the derived model collision terms need to guarantee positivity of the macroscopic fields. In the present work, two new kinetic models are introduced and compared: an approach based on the Shakhov kinetic model and an approach involving an anisotropic Gaussian equilibrium function. The two new models are capable of modelling a binary mixture of monoatomic gases, with updated definitions for the relaxation parameters and target species velocities and temperature. Both methods account for separate species-mean velocity such that the species diffusion and velocity drift are accurately represented. The key contribution of the models is the exact recovery of the Fick, Newton and Fourier laws in the continuum limit, while preserving positive temperature fields and crucial properties of the Boltzmann equation. The profile of a normal shock wave is inspected under various flow conditions to numerically validate the two models. The results show improvement upon comparison with a model, which has two correct transport coefficients, and demonstrate the ability to reliably model inert gas mixtures.

• Item Type: Articles
• Additional Information: The authors would like to acknowledge the financial support provided by the University of Glasgow. Results were obtained using the EPSRC funded ARCHIE-WeSt High Performance Computer (www.archie-west.ac.uk). EPSRC grant no. EP/K000586/1.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steijl, Dr Rene and Todorova, Blaga
• Authors: Todorova, B. N., and Steijl, R.
• College/School: College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
• Journal Name: European Journal of Mechanics - B/Fluids
• Publisher: Elsevier
• ISSN: 0997-7546
• ISSN (Online): 1873-7390
• Published Online: 14 April 2019
• Copyright Holders: Copyright © 2019 Elsevier
• First Published: First published in European Journal of Mechanics - B/Fluids 76:390-402
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher