Automatic selection algorithm of interpolation points on aeroelastic coupling interface
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摘要:
气动弹性模拟中，为了降低耦合数据插值传递矩阵规模，提升耦合数据传递效率，通常采用选取部分界面网格点构建插值矩阵的策略。目前，耦合界面插值点主要通过人工手动的方式选取得到，在网格点数量较大情况下存在耗时长、易错选/漏选的问题。针对手动选点带来的问题，发展了一种耦合界面插值点自动选择算法，通过边界网格点提取、边界网格点精简2步实现。基于结构有限元模型中网格单元的节点信息，建立单元之间的邻接信息，根据邻接信息对网格点进行分类，提取结构有限元模型的边界网格点。基于径向基函数(RBF)插值，借鉴网格变形中的贪婪选点策略，逐步将几何表征误差最大的点选入插值点集，实现边界网格点的精简和耦合界面插值点集的构建。通过飞翼外形结构有限元模型对所提算法及参数影响进行测试，并将算法应用于AGARD445.6和DLR-F6模型的静气动弹性耦合模拟中，测试及模拟结果表明：所提算法能够实现耦合界面插值点的自动选取，并获得与手动选点方式一致的气动弹性计算结果。
Abstract:The method of selecting partial grid points on the coupling interface to build the interpolation matrix of coupling data is typically used in aeroelastic modeling in order to decrease the interpolation matrix’s scale and increase its efficiency. Now, the selection of the interpolation points from the coupling interface is achieved manually and has issues of high time cost, wrong selection or missing selection when the number of grid points is large. In order to solve the problem caused by manual selection, a two-step automatic selection algorithm of the interpolation points on the coupled interface, which is based on the extraction and reduction of boundary grid points, is presented. Firstly, the adjacent information of grid elements is reconstructed through the node index data of each element in the structural finite element model. The grid points are classified into boundary and interior points with the use of the adjacent information and the boundary grid points are extracted directly. Secondly, the boundary grid points are reduced to create the coupling interface’s interpolation point set using the greedy algorithm and radial basis function (RBF) interpolation, which is frequently used in grid deformation. The grid point with the largest interpolation error is then gradually added to the point set. Finally, the automatic selection algorithm is tested to investigate the influence of parameters through the flying wing case and applied to the static aeroelasticity simulation of AGARD445.6 and DLR-F6 models. The test and simulation data demonstrate that the present algorithm can construct the interpolation point set of the coupling interface automatically and obtain approximate simulation results as manual selection.
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图 4 飞翼外形结构有限元模型边界网格点提取
Figure 4. Boundary mesh points extraction of finite element model for flying wing aircraft structure
图 5 飞翼外形结构有限元模型边界网格点精简（不同选点数量）
Figure 5. Boundary mesh points reduction of finite element model for flying wing aircraft structure (different numbers of selected points)
图 6 飞翼外形结构有限元模型边界网格点精简（不同基函数）
Figure 6. Boundary mesh points reduction of finite element model for flying wing aircraft structure (different basis functions)
图 7 飞翼外形结构有限元模型边界网格点精简（不同基函数支撑半径）
Figure 7. Boundary mesh points reduction of finite element model for flying wing aircraft structure (different support radius of basis functions)
图 10 AGARD445.6模型变形计算结果
Figure 10. Computational deformation results of AGARD445.6 model
图 11 AGARD445.6模型压力系数计算结果
Figure 11. Computational pressure coefficient results of AGARD445.6 model
图 15 DLR-F6模型压力系数计算结果
Figure 15. Computational pressure coefficient results of DLR-F6 model
表 1 紧支型基函数
Table 1. Compact basis function
类型 定义 Wendland’s C0 (C0) $ \varphi \left(\eta \right)={\left(1-\eta \right)}^{2} $ Wendland’s C2 (C2) $ \varphi \left(\eta \right)={\left(1-\eta \right)}^{4}\left(4\eta +1\right) $ Wendland’s C4 (C4) $ \varphi \left(\eta \right)={\left(1-\eta \right)}^{6}\left(35{\eta }^{2}+18\eta +3\right) $ Wendland’s C6 (C6) $ \varphi \left(\eta \right)={\left(1-\eta \right)}^{8}\left(35{\eta }^{3}+25{\eta }^{2}+8\eta +1\right) $ 
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