Geodesic
Rarefied gas flow through a pipe of variable square cross section into vacuum
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 8, pp. 1402-1411

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The kinetic S-model is used to study the steady rarefied gas flow through a long pipe of variable cross section joining two tanks with arbitrary differences in pressure and temperature. The kinetic equation is solved numerically by applying a second-order accurate conservative method on an unstructured mesh. The basic quantity to be computed is the gas flow rate through the pipe. The possibility of finding a solution based on the assumption of the plane cross sectional flow is also explored. The resulting solutions are compared with previously known results. 
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     author = {V. A. Titarev and S. V. Utyuzhnikov and E. M. Shakhov},
     title = {Rarefied gas flow through a pipe of variable square cross section into vacuum},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
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     number = {8},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_8_a14/}
}
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V. A. Titarev; S. V. Utyuzhnikov; E. M. Shakhov. Rarefied gas flow through a pipe of variable square cross section into vacuum. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 8, pp. 1402-1411. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_8_a14/