微重力下圆管毛细流动解析近似解研究

应用同伦分析法研究微重力环境下圆管毛细流动解析近似解问题, 给出了级数解的表达公式. 不同于其他解析近似方法, 该方法从根本上克服了摄动理论对小参数的过分依赖, 其有效性与所研究的非线性问题是否含有小参数无关, 适用范围广. 同伦分析法提供了选取基函数的自由, 可以选取较好的基函数, 更有效地逼近问题的解, 通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度, 同伦分析法为圆管毛细流动问题的解析近似求解开辟了一个全新的途径. 通过具体算例, 将同伦分析法与四阶龙格库塔方法数值解做了比较, 结果表明, 该方法具有很高的计算精度. 关键词： 圆管 微重力 毛细流动 同伦分析法

The analytical approximate solutions of capillary flow in circular tubes under microgravity

The capillary flow in a circular tube under microgravity environment is investigated by the homotopy analysis method (HAM), and the approximate analytical solution in the form of series solution is obtained. Different from other analytical approximate methods, the HAM is totally independent of small physical parameters, and thus it is suitable for most nonlinear problems. The HAM provides us a great freedom to choose basis functions of solution series, so that a nonlinear problem can be approximated more effectively, and it adjusts and controls the convergence region and the convergence rate of the series solution through introducing auxiliary parameter and the auxiliary function. The HAM hews out a new approach to the analytical approximate solutions of capillary flow in a circular tube. Through the specific example and comparing homotopy approximate analytical solution with the numerical solution which is obtained by the fourth-order Runge-Kutta method, the computed result indicate that this method has the good computational accuracy.