New Method for Mesh Moving Based on Radial Basis Function Interpolation

Abstract

A new point-by-point mesh movement algorithm is developed for the deformation of unstructured grids. The method is based on using radial basis function, RBFs, to interpolate the displacements of the boundary nodes to the whole flow mesh. A small system of equations has to be solved, only involving the nodes on the boundary of the flow domain. Because no grid-connectivity information is needed, this method is very easy to implement, even for 3D applications. There are various RBFs available in literature that can be used for the new method. Therefore, the new algorithm is tested with several RBFs for a variety of problems to investigate which RBF produces the best meshes and which one is the most efficient. The method can handle large mesh deformations caused by translations, rotations and deformations of the boundary of the domain. However, the performance depends on the used RBF. The best accuracy and robustness are obtained with the thin plate spline. When efficiency is more important, a polynomial RBF with compact support is the best choice.