Evolution to a steady state for a rarefied gas flowing from a tank into a vacuum through a plane channel |
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Authors: | N A Konopel’ko E M Shakhov |
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Institution: | 1.Moscow Institute of Physics and Technology, Dolgoprudnyi,Moscow oblast,Russia;2.Bauman Moscow State Technical University,Moscow,Russia;3.Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,”,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | 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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