A consistent kinetic model for a two-component mixture of polyatomic molecules

TL;DR

This paper develops a consistent kinetic model for a two-component mixture of polyatomic molecules, capturing energy transfer and internal degrees of freedom, with proven physical properties and numerical reduction techniques.

Contribution

It introduces a novel ES-BGK based kinetic model for polyatomic mixtures with multiple internal energy modes, ensuring physical consistency and enabling macroscopic law derivation.

Findings

Proves conservation, positivity, and H-theorem for the model.

Demonstrates convergence to a Maxwellian equilibrium.

Applies Chu reduction for numerical simulations.

Abstract

We consider a multi component gas mixture with translational and internal energy degrees of freedom assuming that the number of particles of each species remains constant. We will illustrate the derived model in the case of two species, but the model can be easily generalized to multiple species. The two species are allowed to have different degrees of freedom in internal energy and are modelled by a system of kinetic ES-BGK equations featuring two interaction terms to account for momentum and energy transfer between the species. We prove consistency of our model: conservation properties, positivity of the temperature, H-theorem and convergence to a global equilibrium in the form of a global Maxwell distribution. Thus, we are able to derive the usual macroscopic conservation laws. For numerical purposes we apply the Chu reduction to the developed model for polyatomic gases and give an application for a gas consisting of a mono atomic and a diatomic species.