Geodesic
Evolution to a steady state for a rarefied gas flowing from a tank into a vacuum through a plane channel
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 10, pp. 1722-1733

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A kinetic equation (S-model) is used to solve the nonstationary problem of a monatomic rarefied gas flowing from a tank of infinite capacity into a vacuum through a long plane channel. Initially, the gas is at rest and is separated from the vacuum by a barrier. The temperature of the channel walls is kept constant. The flow is found to evolve to a steady state. The time required for reaching a steady state is examined depending on the channel length and the degree of gas rarefaction. The kinetic equation is solved numerically by applying a conservative explicit finite-difference scheme that is firstorder accurate in time and second-order accurate in space. An approximate law is proposed for the asymptotic behavior of the solution at long times when the evolution to a steady state becomes a diffusion process. 
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     author = {N. A. Konopel'ko and E. M. Shakhov},
     title = {Evolution to a steady state for a rarefied gas flowing from a tank into a vacuum through a plane channel},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1722--1733},
     publisher = {mathdoc},
     volume = {57},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_10_a9/}
}
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N. A. Konopel'ko; E. M. Shakhov. Evolution to a steady state for a rarefied gas flowing from a tank into a vacuum through a plane channel. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 10, pp. 1722-1733. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_10_a9/