Curved mesh generation using radial basis functions

A method for generating curved meshes from linear meshes is presented in this work. The method is designed to generate a curved mesh for any type of grid in a computationally inexpensive and numerically robust manner. In this method, high-order nodes are first placed in the linear mesh, the high-order boundary nodes are then relocated to the true boundary, and finally, the high-order interior nodes are moved using radial basis function (RBF) interpolation based on the motion of the high-order boundary nodes. The developed method is used to generate curved meshes for two- and three-dimensional geometries. The numerical experiments indicate that the RBF-interpolation method is much better than the prevalent linear-elasticity methods for generating high-order curved meshes judging by curved-mesh quality, computing cost, and ease of implementation.