# Macroscopic Transport Equations for Rarefied Gas Flows

## Approximation Methods in Kinetic Theory

• Henning Struchtrup
Textbook

Part of the Interaction of Mechanics and Mathematics book series (IMM)

1. Front Matter
Pages I-XIV
2. Henning Struchtrup
Pages 1-13
3. Henning Struchtrup
Pages 15-26
4. Henning Struchtrup
Pages 27-51
5. Henning Struchtrup
Pages 53-74
6. Henning Struchtrup
Pages 75-85
7. Henning Struchtrup
Pages 87-107
8. Henning Struchtrup
Pages 109-121
9. Henning Struchtrup
Pages 123-143
10. Henning Struchtrup
Pages 145-160
11. Henning Struchtrup
Pages 161-173
12. Henning Struchtrup
Pages 175-195
13. Henning Struchtrup
Pages 197-228
14. Back Matter
Pages 229-258

### Introduction

The well known transport laws of Navier-Stokes and Fourier fail for the simulation of processes on lengthscales in the order of the mean free path of a particle that is when the Knudsen number is not small enough. Thus, the proper simulation of flows in rarefied gases requires a more detailed description.

This book discusses classical and modern methods to derive macroscopic transport equations for rarefied gases from the Boltzmann equation, for small and moderate Knudsen numbers, i.e. at and above the Navier-Stokes-Fourier level. The main methods discussed are the classical Chapman-Enskog and Grad approaches, as well as the new order of magnitude method, which avoids the short-comings of the classical methods, but retains their benefits. The relations between the various methods are carefully examined, and the resulting equations are compared and tested for a variety of standard problems.

The book develops the topic starting from the basic description of an ideal gas, over the derivation of the Boltzmann equation, towards the various methods for deriving macroscopic transport equations, and the test problems which include stability of the equations, shock waves, and Couette flow.

### Keywords

Asymptotic Methods Boltzmann Equation Chapman-Enskog Expansion Grad Moment Method Kinetic Theory Knudsen Layers Microscale Flows Shock Waves Transport simulation

#### Authors and affiliations

• Henning Struchtrup
• 1
1. 1.Department of Mechanical Engineering and Institute for Integrated Energy SystemsUniversity of VictoriaVictoriaCanada

### Bibliographic information

• DOI https://doi.org/10.1007/3-540-32386-4
• Copyright Information Springer-Verlag Berlin Heidelberg 2005
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Engineering
• Print ISBN 978-3-540-24542-1
• Online ISBN 978-3-540-32386-0
• Series Print ISSN 1860-6245
• Series Online ISSN 1860-6253
• Buy this book on publisher's site