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.
General
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