High-order mesh generation using RBFs based on geometrical similarity

This paper proposes a method to generate high-order curvilinear mesh using compact radial basis function (RBF) interpolation with optimized support radius. We start with an initial high-order linear mesh, and relocate the boundary nodes to their true positons on the true curved geometry. Then the rest mesh nodes are moved using RBF interpolation based on boundary nodes displacement. However, if one assigns identical support radius to all control points, the interpolation might result in poor-quality or even invalid mesh elements. In this article, we present an optimization process to determine a proper set of support radius. Additionally, a novel and fast curved mesh quality estimation based on geometrical similarity between linear and curvilinear mesh element is used to speed up the optimization process. A number of examples including highly stretched boundary layer meshes of complex geometries are tested, the results illustrate that our method is able to produce high quality curved meshes with low computational cost.