Geodesic
Unsteady rarefied gas flow in a microchannel driven by a pressure difference
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3, pp. 476-489

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The kinetic S-model is used to study the unsteady rarefied gas flow through a plane channel between two parallel infinite plates. Initially, the gas is at rest and is separated by the plane $x=0$ with different pressure values on opposite sides. The gas deceleration effect of the channel walls is studied depending on the degree of gas rarefaction and the initial pressure drop, assuming that the molecules are diffusely reflected from the boundary. The decay of the shock wave and the disappearance of the uniform flow region behind the shock wave are monitored. Special attention is given to the gas mass flux through the cross section at $x=0$, which is computed as a function of time. The asymptotic behavior of the solution at unboundedly increasing time is analyzed. The kinetic equation is solved numerically by applying a conservative finite-difference method of second-order accuracy in space. 
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     title = {Unsteady rarefied gas flow in a microchannel driven by a pressure difference},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a14/}
}
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N. A. Konopel'ko; V. A. Titarev; E. M. Shakhov. Unsteady rarefied gas flow in a microchannel driven by a pressure difference. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3, pp. 476-489. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a14/