Geodesic
Three-dimensional fluid equations from distribution function with discontinuity in velocity space
Matematičeskoe modelirovanie, Tome 18 (2006) no. 4, pp. 118-128

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The system of hydrodynamic-type equations for a stratified gas in gravity field is derived from BGK equation by method of piecewise continuous distribution function. The obtained system of the equations generalizes the Navier–Stokes one at arbitrary Knudsen numbers. The problem of a wave disturbance propagation in a rarefied gas is explored. The verification of the model is made for a limiting case of a homogeneous medium. The phase velocity and attenuation coefficient values are in an agreement with former fluid mechanics theories and, in the range of the Knudsen number around 1, even more close to experiment and to kinetics-based results. 
@article{MM_2006_18_4_a9,
     author = {S. B. Leble and M. A. Solovchuk},
     title = {Three-dimensional fluid equations from distribution function with discontinuity in velocity space},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {118--128},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_4_a9/}
}
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S. B. Leble; M. A. Solovchuk. Three-dimensional fluid equations from distribution function with discontinuity in velocity space. Matematičeskoe modelirovanie, Tome 18 (2006) no. 4, pp. 118-128. http://geodesic.mathdoc.fr/item/MM_2006_18_4_a9/