一种基于径向基函数和峰值选择法的高效网格变形技术

基于径向基函数的网格变形方法因其具有诸多优点，而被广泛应用于气动外形优化设计等领域。对于大规模网格或复杂构型，该方法所需计算量是难以承受的。为了提高网格变形效率，可以通过减少建立插值模型所需支撑点数目来实现。为此，提出一种高效的选点算法--峰值选择法。该算法在选点过程的每个迭代步中对边界节点处的误差进行分析，从物面节点中选取多个峰值点来更新支撑点集，减少迭代步数，提高选点效率。在该算法的基础上，实现了网格的高效变形。三段翼型的网格变形算例证明：该方法可以在保证网格质量的同时实现复杂网格的变形。以DLR-F6复杂模型（约1 000万网格）的刚性运动和弹性大变形为算例对该方法的变形效率和变形后网格质量做了进一步评估：当相对误差设置为5.0×10^-7时，在保证变形后网格质量的前提下，该方法变形效率最快比传统贪婪算法提高了13倍，其中在选点效率方面最快提高了31倍。

An efficient mesh deformation method based on radial basis functions and peak-selection method

The mesh deformation based on radial basis functions (RBFs) have many advantages, thus it has been widely employed in aerodynamic optimization design as well as other fields. For large-scale meshes or complex configurations, the expense of deforming by RBFs is unbearable. Reducing the number of support points that build the RBFs model provides an alternative to improve the efficiency of the deformation. Thus, the peak-selection method is developed to efficiently select support points. The method can select multiple peak points from boundary nodes to update the support point set through analyzing the interpolation error of boundary nodes at each iterative step. Therefore, the peak-selection method can significantly reduce the iterative steps and greatly improve the efficiency of selecting support points set. Finally, an RBFs interpolation model is established using the specified support point set to calculate the displacement of the volume mesh points. The deformation of a three element airfoil validates the developed method under good deformation conditions. Further, the DLR-F6 geometry with ten million mesh points under rigid motion and flexible deformation is deformed. The results demonstrate that the deforming and the selecting efficiencies of the peak-selection method are improved by 13 times and 31 times compared with the conventional greedy method on the premise of a good quality when setting relative error as 5.0×10^-7.