Henning Struchtrup Macroscopic
Transport Equations for Rarefied Gas Flows Approximation Methods in Kinetic
Theory Interaction of Mechanics and Mathematics Series Springer,
Heidelberg 2005 258 pages, ISBN:
3-540-24542-1 The Interaction
in Mechanics and Mathematics (IMM) series publishes advanced
textbooks and introductory scientific monographs devoted to modern research
in the wide area of mechanics. The authors are distinguished specialists with
international reputation in their field of expertise. The books are
intended to serve as modern guides in their fields and anticipated to
be accessible to advanced graduate students. IMM books are planned to
be comprehensive reviews developed to the cutting edge of their
respective field and to list the major references.
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.
Order
from Springer
or
amazon.com
