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

J Haack¹, C Hauck², C Klingenberg³

¹Los Alamos National Laboratory, Los Alamos, NM 87545 USA.

Journal of Statistical Physics

|November 1, 2021

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.

Keywords:

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

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