An Efficient and Precise Hybrid Method for Mesh Deformation

Unstructured mesh deformation is an effective way to automatically generate mesh after geometric shape changes such as fluid–structure interaction simulation or aerodynamic shape optimization. The radial basis function method is one of the best mesh deformation methods, which takes into account both computational time and deformation ability. However, the current existing methods are confronted by the contradiction between computational efficiency and deformation accuracy. In this paper, a hybrid deformation method combining the radial basis function and distance-weighted function is proposed, which can effectively reduce computing cost and eliminate deformation error. Firstly, based on the radial basis function method with data reduction scheme, an efficient equidistant sampling method for points selection independent of the specific form of deformation is proposed, and a sampling algorithm based on bisection is devised to make the number of sample points quickly approach the expected value. Secondly, a compact distance-weighted function deformation method is developed, which is used to diffuse the deformation errors of boundary mesh points directly to interior mesh points in order to completely eliminate the deformation errors. Finally, two configurations, AGARD 445.6 wing and HIRENASD wing, are used to test the deformation capability of the hybrid method and the computing time of several key processes. The results show that the hybrid method can accurately realize large mesh deformation with a maximum displacement up to 50% span length, and at the same time, the mesh deformation can be completed with a single core in about 100 s for millions of mesh points, which indicates that the hybrid method in this paper has the ability to be applied to complicated configurations in real engineering.