Journal of Statistical Physics

, Volume 83, Issue 5–6, pp 1021–1065

Moment closure hierarchies for kinetic theories

  • C. David Levermore

DOI: 10.1007/BF02179552

Cite this article as:
Levermore, C.D. J Stat Phys (1996) 83: 1021. doi:10.1007/BF02179552


This paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory. The first member of the hierarchy is the Euler system, which is based on Maxwellian velocity distributions, while the second member is based on nonisotropic Gaussian velocity distributions. The closure proceeds in two steps. The first ensures that every member of the hierarchy is hyperbolic, has an entropy, and formally recovers the Euler limit. The second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct Navier-Stokes behavior. This is achieved through the introduction of a generalization of the BGK collision operator. The simplest such system in three spatial dimensions is a “14-moment” closure, which also recovers the behavior of the Grad “13-moment” system when the velocity distributions lie near local Maxwellians. The closure procedure can be applied to a general class of kinetic theories.

Key Words

Kinetic theory moment closures hyperbolic systems entropy, BGK 

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • C. David Levermore
    • 1
  1. 1.Department of Mathematics and Program in Applied MathematicsUniversity of ArizonaTucson

Personalised recommendations