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

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.

A BGK Model for Gas Mixtures of Polyatomic Molecules Allowing for Slow and Fast Relaxation of the Temperatures

“…In this section we will present the model from the literature for one species described in [14]. For the convenience of the reader, we briefly repeat it here.…”

“…For the convenience of the reader, we briefly repeat it here. For more details and motivation for the choice of the model see [14]. Let x ∈ R d and v ∈ R d , d ∈ N be the phase space variables and t ≥ 0 the time.…”

“…In this section we will present a model from the literature for gas mixtures of polyatomic molecules. It is an extension of the model described in section 2.2 and is presented in [14]. For the convenience of the reader, we briefly repeat it here.…”

“…In this paper, we want to analyse the principles of realizing this in the case of different existing BGK models for polyatomic molecules in the literature, both for one species and for gas mixtures. In the case of one species, the first one is the model by Andries, Le Tallec, Perlat and Perthame [1], the second one is the model of Klingenberg, Pirner and Puppo [14] reduced to one species and the last one, the model of Bernard, Iollo, Puppo in [4]. In the case of gas mixture, we analyse the model presented in [14].…”

“…The outline of the paper is as follows: in section 2 we will present three existing models for one species [1], [14] and [4] in the literature, prove the convergence rates to equilibrium in the space homogeneous case and discuss the physical validity of the three models. In section 3 we will present an existing model for gas mixtures [14] in the literature, prove the convergence rate to equilibrium in the space homogeneous case and discuss the physical validity. In section 4, we present a new model for gas mixtures of polyatomic molecules which has a larger physical validity and prove the H-theorem and the convergence rate to equilibrium for this new model.…”