微重力环境下无限长柱体内角毛细流动解析近似解研究

应用同伦分析法研究无限长柱体内角毛细流动解析近似解问题,给出了级数解的递推公式.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,同伦分析法为内角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.

Analytical approximations for capillary flow in interior corners of infinite long cylinder under microgravity

The capillary flow in interior corners of infinite long cylinder under microgravity environment is investigated by the homotopy analysis method (HAM). Different from other approximate computational method, the HAM totally depends on small physical parameters, and thus it is suitable for most nonlinear problems. The HAM provides us with a great freedom to choose basis functions of solution series, so that a nonlinear problem can be more effectively approximated. The HAM can adjust and control the convergence region and the convergence rate of the series solution through introducing auxiliary parameter and the auxiliary function. The computed result indicates that this method has the advantage of high accuracy.