A Consistent BGK Model with Velocity-Dependent Collision Frequency for Gas Mixtures

J Stat Phys. 2021;184(3):31. doi: 10.1007/s10955-021-02821-2. Epub 2021 Sep 12.


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.

Keywords: BGK approximation; Entropy minimization; Kinetic model; Multi-fluid mixture; Plasma physics; Velocity-dependent collision frequency.