基于错误函数的四面体网格优化方法  

Optimization of tetrahedral mesh based on error function

作　　者：刘厚林[1] 路明臻[1] 董亮[1] 任芸[1] 舒敏骅[1] 

机构地区：[1]江苏大学流体机械工程技术研究中心,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2011年第1期60-64,共5页Journal of Jiangsu University：Natural Science Edition

基　　金：国家杰出青年基金资助项目(50825902);国家"863"计划项目(2006AA05Z250)

摘　　要：通过对现有网格优化算法及网格质量函数的研究,选用常见的四面体网格质量函数,同时考虑边质量约束,推导出了错误函数,基于这个错误函数对四面体网格进行优化.采用错误函数作为基于优化算法光顺的目标函数,并通过应用变尺度法(BFGS)求解错误函数最小值问题对四面体网格进行光顺.将改进的基于优化算法的光顺与拓扑优化算法中的点重叠技术和交换技术相结合,用以解决前沿推进法(AFT)和Delaunay三角化方法产生的非孤立劣质单元问题.经过某双流道叶轮算例进行验证,结果表明:优化后网格质量趋近于0的最差单元基本被消除,同时网格的整体质量也得到了显著提高.With the development of mesh technique,mesh optimization becomes more and more important.Several usual mesh optimization methods were briefly reviewed.According to the study of used measurement for tetrahedral element quality,an error function was introduced.The mesh was optimized based on the error function.The error function was adopted as the composite function of the optimization-based smoothing.The smoothing can be calculated by minimizing the error function using Broyden Fletcher Goldfarb Shanno（BFGS） method.The poor-quality elements generated by the mesh generation algorithms of advancing front technique（AFT） and Delaunay Triangulation were eliminated combining the optimization-based smoothing topology optimization.The point collapsing and swapping technology was selected to the topology optimization.The practical application of the optimization algorithm for a impeller of a double channel pump shows that the worst mesh elements can be eliminated and the whole mesh quality can be improved markedly.

关 键 词：四面体网格 网格优化 错误函数 拓扑优化 交换技术 

分 类 号：TH311[机械工程—机械制造及自动化]