Efficient and Robust Unstructured Grid Deformation Method Based on Radial Basis Function and Delaunay Graph Mapping

The efficiency and robustness of grid deformation methods have a significant impact on the entire research process for aerodynamic shape optimization, aeroelastic calculation, and other issues involving updating the flow field calculation grid. The radial basis function (RBF) method can ensure high grid quality, but its efficiency is extremely low when there are many spatial and surface grids. On the contrary, the Delaunay graph mapping (DGM) method has high efficiency, but the grid quality rapidly decreases during large deformations. Therefore, this paper combined the advantages of both RBF and DGM methods and utilized grid aggregation to automatically generate background grids. By using the RBF method to update the background grids, the problem of DGM method not being suitable for large deformation of object surfaces was solved. By using the DGM method to improve deformation efficiency, an efficient and robust grid deformation method was established. By comparison, this method can maintain a basic consistency with the RBF method in terms of grid deformation quality. For three-dimensional examples, the grid deformation efficiency can be improved by more than 90% compared to the RBF method.