【作者】 刘玲； 李靖； 廖世俊；

【Author】 LIU Ling;LI Jing;LIAO Shi-jun;School of Naval Architecture,Ocean and Engineering,Shanghai Jiao Tong University;State Key Laboratory of Ocean Engineering;

【机构】 上海交通大学船舶海洋与建筑工程学院； 海洋工程国家重点实验室；

【摘要】 超声速边界层流动是高速空气动力学的一个值得关注的主要问题,本研究应用同伦分析方法对超声速层流边界层的问题进行了研究,获得了一个收敛的级数解。值得注意的是,所得到的级数解在整个空间域上是有效的。另外,这种级数解在马赫数高达40～50时仍然能保证收敛性。通过和数值解对比发现,同伦分析方法所获的收敛结果与数值解是高度一致的,这一点验证了同伦分析法的有效性。此项研究的结果对实际工程领域内超音速问题具有参考性价值。同时说明同伦分析方法具有很大的潜力去求解气动力学上更复杂的流动问题。更多还原

【Abstract】 Supersonic boundary layer flow is one of the main problems in high speed aerodynamics.In this paper,homotopy analysis method is used to study the supersonic laminar boundary layer.A convergent series solution is obtained.It is worth noting that the series solutions obtained in this paper are valid in the whole spatial domain.In addition,the series solution can guarantee convergence even for the high Mach number up to 40-50.Compared with the numerical solution,it is found that the convergence results obtained by homotopy analysis method are highly consistent with the numerical solution,which verifies the effectiveness of homotopy analysis method.The results in this study provide reference value for supersonic problems in practical engineering field.It also shows that homotopy analysis method has great potential to solve more complex flow problems in aerodynamics.更多还原