# 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:

- 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}

}

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