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


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.


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



Los Alamos Report LA-UR-16-28001. This manuscript has been authored, in part, by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( The research of CH was sponsored by the Office of Advanced Scientific Computing Research and performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725. The research of JH and MSM was performed in part under the auspices of the U.S. Department of Energy by Los Alamos National Laboratory under Contract DE-AC52-06NA25396.


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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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