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Title: The Boltzmann equation in the difference formulation

Abstract

First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.

Authors:
 [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1184176
Report Number(s):
LLNL-TR-671181
TRN: US1500306
DOE Contract Number:  
AC52-07NA27344
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOLTZMANN EQUATION; THERMAL CONDUCTIVITY; APPROXIMATIONS; COLLISIONS; CHAPMAN-ENSKOG THEORY; SERIES EXPANSION; GASES

Citation Formats

Szoke, Abraham, and Brooks III, Eugene D. The Boltzmann equation in the difference formulation. United States: N. p., 2015. Web. doi:10.2172/1184176.
Szoke, Abraham, & Brooks III, Eugene D. The Boltzmann equation in the difference formulation. United States. doi:10.2172/1184176.
Szoke, Abraham, and Brooks III, Eugene D. Wed . "The Boltzmann equation in the difference formulation". United States. doi:10.2172/1184176. https://www.osti.gov/servlets/purl/1184176.
@article{osti_1184176,
title = {The Boltzmann equation in the difference formulation},
author = {Szoke, Abraham and Brooks III, Eugene D.},
abstractNote = {First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.},
doi = {10.2172/1184176},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2015},
month = {5}
}

Technical Report:

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