Doi Toshiyuki
Department of Applied Mathematics and Physics, Graduate School of Engineering, Tottori University, Tottori 680-8552, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Feb;83(2 Pt 2):026311. doi: 10.1103/PhysRevE.83.026311. Epub 2011 Feb 28.
Plane Poiseuille flow of a rarefied gas, which flows horizontally in the presence of strong gravitation, is studied based on the Boltzmann equation. Applying the asymptotic analysis for a small variation in the flow direction [Y. Sone, Molecular Gas Dynamics (Birkhäuser, 2007)], the two-dimensional problem is reduced to a one-dimensional problem, as in the case of a Poiseuille flow in the absence of gravitation, and the solution is obtained in a semianalytical form. The reduced one-dimensional problem is solved numerically for a hard sphere molecular gas over a wide range of the gas-rarefaction degree and the gravitational strength. The presence of gravitation reduces the mass flow rate, and the effect of gravitation is significant for large Knudsen numbers. To verify the validity of the asymptotic solution, a two-dimensional problem of a flow through a long channel is directly solved numerically, and the validity of the asymptotic solution is confirmed.
基于玻尔兹曼方程，研究了在强引力作用下水平流动的稀薄气体的平面泊肃叶流动。应用流动方向微小变化的渐近分析方法[Y. 索尼，《分子气体动力学》（比尔克豪泽出版社，2007年）]，与无引力情况下的泊肃叶流动情形一样，二维问题简化为一维问题，并以半解析形式得到解。针对硬球分子气体，在很宽的气体稀薄度和引力强度范围内，对简化后的一维问题进行了数值求解。引力的存在降低了质量流率，且对于大克努森数，引力效应显著。为验证渐近解的有效性，对通过长通道的流动二维问题直接进行了数值求解，从而证实了渐近解的有效性。
