Radial basis function mesh deformation based on dynamic control points

Abstract

Radial basis function (RBF) interpolation is a robust mesh deformation method, which has the main property of interpolating the displacements of mesh boundary points to the internal points through RBF. However, this method is computationally intensive, especially for problems with large number of grids. To handle this problem, a data reduction RBF method has been developed in literature. By using greedy algorithm, only a small subset of mesh boundary points is selected as the control point set to perform mesh deformation. Subsequently, much few boundary points are needed to approximate the shape of geometry and the computational cost of data reduction RBF method is much lower than the original RBF. Despite the referred benefits, this method incurs the loss of geometry precision especially at boundaries where large deformation happens, which results into the decline of deformation capacity. To further improve the data-reduction RBF method, a novel dynamic-control-point RBF (DCP-RBF) mesh deformation method is proposed in this paper, which employing a dynamic set of control points. In each time step of mesh deformation, the neighboring boundary point near the cell with the worst quality is added into the control point set, while the neighboring control point near the cell with the best quality is removed from the control point set. In this way, it is ensured that there are more control points placed around the region with lower mesh quality, where usually large deformation occurs. Consequently, in contrast with the data reduction RBF method, DCP-RBF permits significantly larger mesh deformation with a quite small increase in computational cost. The superiority of the proposed DCP-RBF method is demonstrated through several test cases including both 2D and 3D dynamic mesh applications.