基于径向基函数和Delaunay图映射的高效高鲁棒性的非结构网格变形方法  

Efficient and Robust Unstructured Grid Deformation Method Based on Radial Basis Function and Delaunay Graph Mapping

作　　者：王昊达 刘南 张颖[1] 崔晓春[1] WANG Hao-da;LIU Nan;ZHANG Ying;CUI Xiao-chun(AVIC Aerodynaiviics Research Institute,Shenyang 110034,China)

机构地区：[1]中国航空工业空气动力研究院,辽宁沈阳110034

出　　处：《气体物理》2023年第6期41-54,共14页Physics of Gases

摘　　要：对于气动外形优化、气动弹性计算等涉及更新流场计算网格的问题,网格变形方法的效率和鲁棒性对整个研究过程有显著影响。其中径向基函数(radial basis function,RBF)方法能够保证较高的网格质量,但是当空间及物面网格数量较多时效率极低。而Delaunay图映射(Delaunay graph mapping,DGM)方法效率很高,但在大变形时网格质量会迅速下降。因此,将结合RBF和DGM两种方法的优点,利用网格聚合方法自动生成背景网格,通过RBF方法更新背景网格,解决DGM方法无法适用于物面大变形的问题,利用DGM方法提高变形效率,建立一种高效高鲁棒性网格变形方法。通过对比,网格变形质量方面该方法能够和RBF方法基本保持一致,且对于本文三维网格算例,网格变形效率较RBF方法能够提升90%以上。The efficiency and robustness of grid deformation methods have a significant impact on the entire research process for aerodynamic shape optimization,aeroelastic calculation,and other issues involving updating the flow field calculation grid.The radial basis function(RBF)method can ensure high grid quality,but its efficiency is extremely low when there are many spatial and surface grids.On the contrary,the Delaunay graph mapping(DGM)method has high efficiency,but the grid quality rapidly decreases during large deformations.Therefore,this paper combined the advantages of both RBF and DGM methods and utilized grid aggregation to automatically generate background grids.By using the RBF method to update the background grids,the problem of DGM method not being suitable for large deformation of object surfaces was solved.By using the DGM method to improve deformation efficiency,an efficient and robust grid deformation method was established.By comparison,this method can maintain a basic consistency with the RBF method in terms of grid deformation quality.For three-dimensional examples,the grid deformation efficiency can be improved by more than 90%compared to the RBF method.

关 键 词：径向基函数 Delaunay图映射 网格聚合 网格变形 网格质量 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]