独立覆盖流形法的通用计算公式和通用程序设计——(三)算例验证  

General Formulas and Program Design for Manifold Method Based onIndependent CoversⅢ:Example Verification

作　　者：苏海东[1,2] 宋文硕 龚亚琦 韩陆超[1] 韦玉霞 SU Hai-dong;SONG Wen-shuo;GONG Ya-qi;HAN Lu-chao;WEI Yu-xia(Material and Engineering Structure Department,Changjiang River Scientific Research Institute,Wuhan 430010,China;Research Center of Water Engineering Safety and Disaster Prevention of Ministry of WaterResources,Wuhan 430010,China)

机构地区：[1]长江科学院材料与结构研究所,武汉430010 [2]水利部水工程安全与病害防治中心,武汉430010

出　　处：《长江科学院院报》2025年第4期211-218,共8页Journal of Changjiang River Scientific Research Institute

摘　　要：在前两篇提出的通用计算公式、通用程序设计方法的基础上,通过求解弹性力学运动微分方程、传导方程、波动方程(含稳态和瞬态分析),给出了一至三维包括位移场、温度场、渗流场、声场、静电场和势流场等算例进行全面验证,涵盖了任意形状和任意连接的网格、精确几何边界的模拟及本质边界条件的准确施加、高阶级数逼近、裂纹尖端附近解析级数的应用等独立覆盖流形法的特色功能。最后对全文进行总结,并提出“级数流形元(级数元)”的新名称。Based on the general calculation formulas and programming methods proposed in the previous two articles,we conduct a comprehensive validation across one-to three-dimensional problems.These involve the displacement field,temperature field,seepage field,sound field,electrostatic field,and potential flow field by solving the differential equations of motion in elasticity,the conduction equation,and the wave equation(covering both steady-state and transient analyses).The provided examples demonstrate the distinctive characteristics of the manifold method based on independent covers.These features include the ability to handle meshes of any shape and connection,the accurate simulation of geometric boundaries,the precise application of essential boundary conditions,high-order series approximation,and the use of analytical series near crack tips.Finally,we summarize the entire article and propose a new term“series manifold element(series element)”.

关 键 词：数值流形方法 独立覆盖 偏微分方程 级数解 网格剖分 精确几何 级数流形元 

分 类 号：O241.82[理学—计算数学]