A consistent BGK model with velocity-dependent collision frequency for gas mixtures

TL;DR

This paper introduces a new multi-species BGK model with velocity-dependent collision frequency for gas mixtures, ensuring conservation laws and entropy decay, advancing kinetic modeling accuracy.

Contribution

It derives a novel BGK model with velocity-dependent collision frequency, proves its well-posedness, and establishes an H-Theorem for multi-species gas mixtures.

Findings

Unique solution for the minimization problem under general collision frequencies

Model satisfies an H-Theorem ensuring entropy decay

Characterizes equilibrium states for the model

Abstract

We derive a multi-species BGK model with velocity-dependent collision frequency for a non-reactive, multi-component gas mixture. The model is derived by minimizing a weighted entropy under the constraint that the number of particles of each species, total momentum, and total energy are conserved. We prove that this minimization problem admits a unique solution for very general collision frequencies. Moreover, we prove that the model satisfies an H-Theorem and characterize the form of equilibrium.