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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.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.
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Keywords:
- infinite long cylinder /
- interior corners /
- capillary flow /
- homotopy analysis method
[1] Washburn E W 1921 Physical Review 17 273283
[2] Wang C X, Xu S H, Sun Z W, Hu W R 2010 International Journal of Heat and Mass Transfer 53 18011807
[3] Xu S H, Wang C X, Sun Z W, Hu W R 2007 Journal of the Japan Society of Microgravity Application 24 275278
[4] Dong M, Chatzis I 1995 Journal of Colloid and Interface Science 172 278288
[5] Wei Y X, Chen X Q, Huang Y Y 2011 Science china: Technological Sciences 41 12181224
[6] Weislogel M M 1996 NASA Technical Memorandum. 107364
[7] Liao S J 2006 Beyond perturbation: introduction to the homotopy analysis method (Bei jing: Science Press) p204 (in Chinese) [廖世俊 2006 超越摄动-同伦分析方法导论(北京: 科学出版社)第204页]
[8] Cheng J, Liao S J 2007 Acta Mechanica Sinica 39 715720 (in Chinese) [成均, 廖世俊 2007 力学学报 39 715720]
[9] Liao S J 2003 Journal of Fluid Mechanics 488 189212
[10] Li Y Q, Zhu D W, Li F 2009 Chinese journal of mechanical engineering 45 3740 (in Chinese) [李永强, 朱大巍, 李锋 2009 机械工程学报 45 3740]
[11] Li Y Q, Li F, Zhu D W 2010 Composite Structures 92 11101119
[12] Yuan P X, Li Y Q 2010 Applied Mathematics and Mechanics (EnglishEdition) 31 12931304
[13] Li Y Q, Li F, He Y L 2011 Composite Structures 93 360368
[14] Li Y Q, Zhu D W 2011 Composite Structures 93 880888
[15] Shi Y R, Yang H J 2010 Acta Phys. Sin. 59 6774 (in Chinese) [石玉人, 杨红娟 2010 物理学报 59 6774]
[16] Yang P, Chen Y, Li Z B 2010 Acta Phys. Sin. 59 3668 (in Chinese) [杨沛, 陈勇, 李志斌 2010 物理学报 59 3668]
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[1] Washburn E W 1921 Physical Review 17 273283
[2] Wang C X, Xu S H, Sun Z W, Hu W R 2010 International Journal of Heat and Mass Transfer 53 18011807
[3] Xu S H, Wang C X, Sun Z W, Hu W R 2007 Journal of the Japan Society of Microgravity Application 24 275278
[4] Dong M, Chatzis I 1995 Journal of Colloid and Interface Science 172 278288
[5] Wei Y X, Chen X Q, Huang Y Y 2011 Science china: Technological Sciences 41 12181224
[6] Weislogel M M 1996 NASA Technical Memorandum. 107364
[7] Liao S J 2006 Beyond perturbation: introduction to the homotopy analysis method (Bei jing: Science Press) p204 (in Chinese) [廖世俊 2006 超越摄动-同伦分析方法导论(北京: 科学出版社)第204页]
[8] Cheng J, Liao S J 2007 Acta Mechanica Sinica 39 715720 (in Chinese) [成均, 廖世俊 2007 力学学报 39 715720]
[9] Liao S J 2003 Journal of Fluid Mechanics 488 189212
[10] Li Y Q, Zhu D W, Li F 2009 Chinese journal of mechanical engineering 45 3740 (in Chinese) [李永强, 朱大巍, 李锋 2009 机械工程学报 45 3740]
[11] Li Y Q, Li F, Zhu D W 2010 Composite Structures 92 11101119
[12] Yuan P X, Li Y Q 2010 Applied Mathematics and Mechanics (EnglishEdition) 31 12931304
[13] Li Y Q, Li F, He Y L 2011 Composite Structures 93 360368
[14] Li Y Q, Zhu D W 2011 Composite Structures 93 880888
[15] Shi Y R, Yang H J 2010 Acta Phys. Sin. 59 6774 (in Chinese) [石玉人, 杨红娟 2010 物理学报 59 6774]
[16] Yang P, Chen Y, Li Z B 2010 Acta Phys. Sin. 59 3668 (in Chinese) [杨沛, 陈勇, 李志斌 2010 物理学报 59 3668]
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