Abstract
An “incompressible fluid” model in gas dynamics is developed in the linear approximation. Using the dissipative relaxation time as a characteristic scale, we arrive at another form of the dimensionless Boltzmann equation. In the limiting case of small Knudsen numbers an approximate solution is obtained in the form of a Hilbert multiple-scale asymptotic expansion. It is revealed that for slow, weakly nonisothermal processes the asymptotic expansion for the linearized Boltzmann equation leads in a first stage to equations for the velocity, pressure and temperature that do not contain the density (quasi-incompressible approximation). The density depends on the temperature and can, if necessary, be found from the equation of state. The next-approximation equations contain the Burnett effects, the velocity calculation being reduced to the general problem of finding a vector field from a given divergence and rotation. With reference to a simple case of the heating of a stationary gas in a half-space it is shown that the temperature establishment process is accompanied by gas flow from the wall.
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Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 170–178.
Original Russian Text Copyright © 2005 by Chekmarev.
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Chekmarev, I.B. Certain Aspects of an “Incompressible Fluid“ Model in Gas Dynamics. Fluid Dyn 40, 486–493 (2005). https://doi.org/10.1007/s10697-005-0087-3
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DOI: https://doi.org/10.1007/s10697-005-0087-3