A space-dependent Boltzmann-BGK model for gas mixtures and its hydrodynamic limits

TL;DR

This paper introduces a hybrid Boltzmann-BGK model for gas mixtures that can switch between Boltzmann and BGK operators spatially, ensuring conservation laws and analyzing hydrodynamic limits for different collision regimes.

Contribution

It proposes a space-dependent hybrid kinetic model for gas mixtures, extending classical models by allowing local operator choices and analyzing their hydrodynamic limits.

Findings

Model guarantees conservation of mass, momentum, and energy.

Ensures entropy dissipation and Maxwellian equilibrium sharing common velocity and temperature.

Analyzes hydrodynamic limits in three distinct regimes.

Abstract

We present a hybrid Boltzmann-BGK model for inert mixtures, where each kind of binary interaction may be described by a classical Boltzmann integral or by a suitable relaxation-type operator. We allow also the possibility of changing the option Boltzmann/BGK operator according to the space position. We prove that this model guarantees conservations of species masses, global momentum and energy, as well as the entropy dissipation, leading to the expected Maxwellian equilibria with all species sharing the same mean velocity and the same temperature. We investigate then such mixed kinetic equations in three different hydrodynamic limits: the classical collision dominated regime, a situation with dominant intra-species collisions, and a mixture with heavy and light particles leading to a kinetic-fluid description.