Geodesic
Nonisothermal gas flow in a long channel analyzed on the basis of the kinetic S-Model
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 12, pp. 2246-2260

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The nonisothermal steady rarefied gas flow driven by a given pressure gradient (Poiseuille flow) or a temperature gradient (thermal creep) in a long channel (pipe) of an arbitrary cross section is studied on the basis of the linearized kinetic S-model. The solution is constructed using a high-order accurate conservative method. The numerical computations are performed for a circular pipe and for a cross section in the form of a regular polygon inscribed in a circle. The basic characteristic of interest is the gas flow rate through the channel. The solutions are compared with previously known results. The flow rates computed for various cross sections are also compared with the corresponding results for a circular pipe. 
@article{ZVMMF_2010_50_12_a13,
     author = {V. A. Titarev and E. M. Shakhov},
     title = {Nonisothermal gas flow in a long channel analyzed on the basis of the kinetic {S-Model}},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2246--2260},
     publisher = {mathdoc},
     volume = {50},
     number = {12},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_12_a13/}
}
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V. A. Titarev; E. M. Shakhov. Nonisothermal gas flow in a long channel analyzed on the basis of the kinetic S-Model. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 12, pp. 2246-2260. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_12_a13/