An efficient multiple point selection study for mesh deformation using radial basis functions

The mesh deformation using radial basis functions (RBFs) is widely used in aerodynamic applications in the context of design & optimization and aeroelasticity. One reason is the good performance for test cases requiring only a few number of support points. But in test cases with complex deflection fields, requiring a large number of support points, the performance of the method degenerates. To improve an existing RBFs-based mesh-deformation method, an efficient multiple point selection method has been developed based on the conventional Greedy method. The interpolation error function of the RBFs-based model is analyzed, and multiple points with maximum local error are selected simultaneously into the support set, with which an interpolation model will be finally built to compute the displacements of the volume mesh nodes. To avoid too many redundant points for building the interpolation model, a threshold factor is conceived to limit the number of points selected. The computational cost by the Greedy method, the multi-level data reduction method and the developed method, are theoretically compared. Typical deformation problems are chosen as test cases for demonstrating current implementations, like a ninety-degree rotation of a NACA 0012 airfoil, the adjustment of the position of the slat and the flap of a high-lift airfoil, the bending of the DLR F6 configuration, and the shape modification of a hypersonic Rocket-Based Combined Cycle space vehicle. Further, the effect of the threshold factor is studied. The results show that the developed mesh-deformation method has a better efficiency than the Greedy method and the multi-level data reduction method, especially for test cases with complex deflection fields.