Journal of Statistical Physics

, Volume 168, Issue 4, pp 826–856 | Cite as

A Conservative, Entropic Multispecies BGK Model

  • Jeffrey R. Haack
  • Cory D. Hauck
  • Michael S. Murillo
Article
  • 98 Downloads

Abstract

We derive a conservative multispecies BGK model that follows the spirit of the original, single species BGK model by making the specific choice to conserve species masses, total momentum, and total kinetic energy and to satisfy Boltzmann’s \(\mathcal {H}\)-Theorem. The derivation emphasizes the connection to the Boltzmann operator which allows for direct inclusion of information from higher-fidelity collision physics models. We also develop a complete hydrodynamic closure via the Chapman-Enskog expansion, including a general procedure to generate symmetric diffusion coefficients based on this model. We numerically investigate velocity and temperature relaxation in dense plasmas and compare the model with previous multispecies BGK models and discuss the trade-offs that are made in defining and using them. In particular, we demonstrate that the BGK model in the NRL plasma formulary does not conserve momentum or energy in general.

Keywords

Multispecies flow Transport coefficients Kinetic theory BGK Plasma physics H theorem Boltzmann equation 

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Copyright information

© Springer Science+Business Media, LLC (outside the USA) 2017

Authors and Affiliations

  • Jeffrey R. Haack
    • 1
  • Cory D. Hauck
    • 2
  • Michael S. Murillo
    • 1
    • 3
  1. 1.Los Alamos National LaboratoryNew MexicoUSA
  2. 2.Oak Ridge National LaboratoryOak RidgeUSA
  3. 3.Michigan State UniversityEast LansingUSA

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