| dc.description |
The Boltzmann equation is written in terms of two functions associated
with the gain and loss of a certain type of molecule due to collisions.
Its integral form is then applied to the problem of normal shock structure,
and an iteration technique is used to determine the solution. The first
approximation to the velocity distribution function of the Chapman-Enskog
sequence, which leads to the Navier-Stokes equations, is used to initiate
the iteration scheme. Expressions for the distribution function and the
flow parameters pertinent to the first iteration are derived and show that
the B-G-K model results can be obtained as a special case. This model is
found to be valid in the continuum regime only, and is consequently limited
to the study of strong shocks. In the present treatment the iteration is
carried out on the distribution function and the analysis indicates that
the method is equally valid for variations in both Mach and Knudsen numbers.
Finally, the results of the first approximation are simplified, and expressed
in a form suitable for numerical computation, and the range of their validity
is discussed. The method should be equally suitable for other flow problems
of linear or nonlinear nature. |
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