Evaluation of Radial Basis Functions for the Deformation of Unstructured Meshes

Abstract

The radial basis function (RBF) mesh deformation methodology is used in this paper to impose large deformations on two-dimensional unstructured hybrid meshes around airfoils, including translation and rigid rotation of the airfoil with respect to its original position. It is realized that, for such large deformations, some of the adopted RBFs failed to produce acceptable deformed meshes: the resulting meshes include large areas with overlapping elements. In order to improve the resulting mesh quality the RBF mesh deformation methodology is combined with a Laplacian smoothing operator, which is repeatedly called after the completion of the basic RBF mesh deformation procedure. A widely adopted metric for mesh quality is used to evaluate the quality of the deformed mesh, with and without Laplacian smoothing, for various radial basis functions. Results for unstructured hybrid meshes are presented, demonstrating the effect of the various RBFs as well as the application of Laplacian smoothing, in terms of grid quality metric values.