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.