© 2005

Macroscopic Transport Equations for Rarefied Gas Flows

Approximation Methods in Kinetic Theory


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

Table of contents

  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 161-173
  11. Henning Struchtrup
    Pages 175-195
  12. Henning Struchtrup
    Pages 197-228
  13. Back Matter
    Pages 229-258

About this book


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.


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

Authors and affiliations

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

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