Macroscopic transport equations for rarefied gas flows. Approximation methods in kinetic theory. (English) Zbl 1119.76002

Struchtrup, Henning

Interaction of Mechanics and Mathematics. Berlin: Springer (ISBN 978-3-540-24542-1/pbk). xiv, 258 p. (2005).

This book presents methods to derive macroscopic transport equations for rarefied gases from Boltzmann equation, for small and moderate Knudsen numbers. The main methods presented are Chapman-Enskog and Grad approaches, as well as the order-of-magnitude method, which avoids the shortcomings of classical methods, but retains their benefits. The relations between 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 ideal gas, over the derivation of Boltzmann equation, towards various test problems which include stability of the equations, shock waves and Couette flow.

Reviewer: Agneta Balint (Timişoara)

MSC:

76-02	Research exposition (monographs, survey articles) pertaining to fluid mechanics
76P05	Rarefied gas flows, Boltzmann equation in fluid mechanics
82C40	Kinetic theory of gases in time-dependent statistical mechanics

Keywords:

Chapman-Enskog method; Grad method; order-of-magnitude method

Software:

Mathematica