Kinetic ES-BGK models for a multi-component gas mixture

TL;DR

This paper introduces an extended ES-BGK kinetic model for multi-component inert gas mixtures, ensuring physical consistency and convergence to equilibrium, with potential applications in gas dynamics simulations.

Contribution

It extends existing BGK models by incorporating ES-BGK effects for multi-species gases, maintaining conservation laws and thermodynamic consistency.

Findings

Proves the model's conservation properties.

Establishes positivity of temperatures.

Demonstrates convergence to Maxwellian equilibrium.

Abstract

We consider a multi component mixture of inert gas in the kinetic regime by assuming that the total number of particles of each species remains constant. In this article we shall illustrate our model for the case of two species. To account for thermal effects, we extend a BGK model based on the presence of a collision term for each possible interaction \cite{Pirner} by including ES-BGK effects. We prove consistency of the extended model like conservation properties, positivity of all temperatures, H-theorem and convergence to a global equilibrium in the shape of a global Maxwell distribution.