Geodesic
Kinetic analysis of an isothermal flow in a long microchannel with rectangular cross section
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 7, pp. 1285-1302

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The linearized kinetic BGK model is used to study the steady Poiseuille flow of a rarefied gas in a long channel of rectangular cross section. The solution is constructed using the finite-volume method based on a TVD scheme. The basic computed characteristic is the mass flow rate through the channel. The effect of the relative width of the cross section is examined, and the difference of the solution from the one-dimensional flow between infinite parallel plates is analyzed. The numerical solution is compared to available results and to the analytical solution of the Navier–Stokes equations with no-slip and slip boundary conditions. The limits of applicability of the hydrodynamic solution are established depending on the degree of rarefaction of the flow and on the ratio of the side lengths of the channel cross section. 
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     author = {V. A. Titarev and E. M. Shakhov},
     title = {Kinetic analysis of an isothermal flow in a long microchannel with rectangular cross section},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1285--1302},
     publisher = {mathdoc},
     volume = {50},
     number = {7},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_7_a10/}
}
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V. A. Titarev; E. M. Shakhov. Kinetic analysis of an isothermal flow in a long microchannel with rectangular cross section. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 7, pp. 1285-1302. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_7_a10/