涡片计算的自适应快速多极边界元法研究  

Research on adaptive fast multipole boundary element method for vortex sheet computation

作　　者：顾信忠 李舜酩[1] GU Xin-zhong;LI Shun-ming(Nanjing University of Aeronautics&Astronautics,Nanjing 210016,China;Nanhang Jincheng College,Nanjing 211156,China)

机构地区：[1]南京航空航天大学,南京210016 [2]南京航空航天大学金城学院,南京211156

出　　处：《船舶力学》2020年第8期971-980,共10页Journal of Ship Mechanics

基　　金：国家自然科学基金资助项目“转速大波动机械特征敏感参数提取与评估方法研究”(51675262);国家重点研究和发展项目“新节能环保农用发动机开发”(2016YDF0700800);预研领域基金课题“与转子特征分析、故障特征分析有关”(6140210020116HK02001)。

摘　　要：为了提高涡方法的计算效率,本文将自适应快速多极边界元法引入涡方法中,发展了一种能够快速计算流场中物体表面涡片强度的方法。首先从流场基本方程详细推导了涡片计算的快速多极边界元方程,然后基于自适应树结构,采用预处理GMRES算法设计了涡片强度的计算方法,最后完成了程序化和数值计算。算例的计算结果与精确解、实验值比较吻合,验证了计算方法的正确性和稳定性。数值计算还表明自适应快速多极边界元法可以显著提高计算效率,减少对存储空间的需求。An adaptive fast multipole boundary element method(FMBEM) was introduced into vortex method to develop a fast method for vortex sheet computation. Firstly, the basic formulations of the FMBEM were derived from the Navier-Stokes equations. Based on adaptive tree structure and preconditioned GMRES algorithm, the vortex sheet computation algorithm was designed and programmed. The calculated results of the examples were in accordance with the exact solutions and the experimental values, therefore the validity and stability of the deigned method were verified. Numerical calculation also showed that the adaptive fast multipole boundary element method can significantly improve the computational efficiency, and lower the computer memory requirement.

关 键 词：边界元法 快速多极展开算法 预处理GMRES 涡片计算 涡方法 

分 类 号：O351.2[理学—流体力学]