An efficient parallel mesh deformation technique based on spatially-nested radial basis functions

Efficient mesh deformation methods can significantly improve computational efficiency in fluid structure interaction numerical simulation and aerodynamic shape optimization based on the high-fidelity CFD method. The mesh deformation method based on original Radial Basis Functions (RBF) can result in a significant increase in computational cost when the number of deformation control points increases. The method of reducing RBF modeling calculation time by reducing deformation control points can result in a loss of fitting accuracy. Since the existing deformation methods based on RBF cannot guarantee the computational efficiency and fitting accuracy simultaneously, this paper proposes a Spatially-Nested Radial Basis Function (SN-RBF) model and develops an efficient mesh deformation method based on SN-RBF. The proposed mesh deformation method maintains the accuracy of mesh deformation, while significantly improving the efficiency of mesh deformation. The spatially-nested radial basis function model utilizes multiple spatially overlapping sub models to replace the radial basis function model which has large number of deformation control points, greatly reducing the modeling time of RBF method in mesh deformation. Considering the good parallelism of the proposed method, the strategies for parallel modeling and parallel mesh deformation based on this method have been adopted, further improving the efficiency of mesh deformation. The test cases show that the more modeling sample points, the more significant the improvement in grid deformation efficiency. For the CRM wing-body configuration case, the maximum improvement in modeling efficiency is 16 947 times, and the maximum improvement in mesh deformation efficiency is 5 218 times.