Moment closure hierarchies for kinetic theories

Journal Article · Sat Jun 01 04:00:00 EDT 1996 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF02179552· OSTI ID:476038

Levermore, C D ^[1]

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1. Univ. of Arizona, Tucson, AZ (United States)

This paper presents a systematic nonperturbative 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 non-isotropic 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 beyond 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 {open_quotes}14-moment{close_quotes} closure, which also recovers the behavior of the Grad {open_quotes}13-moment{close_quotes} system when the velocity distributions lie near local Maxwellians. The closure procedure can be applied to a general class of kinetic theories.

• Sponsoring Organization: USDOE
• OSTI ID: 476038
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 5-6 Vol. 83; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
66 PHYSICS
BOLTZMANN STATISTICS
ENTROPY
GASES
GAUSSIAN PROCESSES
KINETIC EQUATIONS
NAVIER-STOKES EQUATIONS
NONLINEAR PROBLEMS