Geodesic
Efficient method for computing rarefied gas flow in a long finite plane channel
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 288-303

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The linearized kinetic S-model is used to study the nonisothermal steady rarefied gas flow driven by differences in pressure and temperature in a plane channel between long finite parallel plates joining two tanks of infinite volume. An efficient composite (asymptotic) method is developed: a one-dimensional asymptotic solution corresponding to an infinitely long channel is constructed in the middle part of the computational domain, while a solution of the two-dimensional kinetic equation matched with the middle-part asymptotic solution is constructed near the ends of the channel. The latter solution is found numerically by a high-order accurate conservative method. The basic quantity to be computed is the gas flow rate through the channel. Characteristic flow features are also investigated. The resulting solutions are compared with previously known results. 
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     author = {V. A. Titarev and E. M. Shakhov},
     title = {Efficient method for computing rarefied gas flow in a long finite plane channel},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {288--303},
     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a11/}
}
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V. A. Titarev; E. M. Shakhov. Efficient method for computing rarefied gas flow in a long finite plane channel. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 288-303. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a11/