Local mesh deformation using a dual-restricted radial basis functions method

Abstract

In order to study the motion of a deformable configuration in the air flow, mesh deformation technology is essentially needed. The radial basis function (RBF) interpolation algorithm is a popular mesh deformation algorithm. For local mesh deformation, such as aeroelastic response simulation of aircraft components and deflection of flight control surface, we do not need to move all grid nodes. On the contrary, only part of the mesh near the deformation boundary needs to be moved. If we can limit the deformation range caused by the RBF method to a small region, the computational cost could be saved. In addition to the consideration of efficiency, another reason is that in the position optimization of aircraft components, we need to keep most of the meshes unchanged to reduce the error caused by mesh inconsistency. In the previous research [24], a restricted RBF interpolation algorithm was constructed and coupled with a multi-level interpolation technique to reduce the volume mesh nodes for global mesh deformation problem. The restricted RBF method is improved in the current research and a so-called dual-restricted RBF algorithm is proposed. This new method constructs a restricting function using the distance both to the moving and static boundaries so that the stationary wall could be preserved exactly. Theoretical analysis and numerical examples also have confirmed that the new algorithm is beneficial to improve the efficiency of mesh deformation process compared with the restricted RBF algorithm because mesh nodes near the stationary boundary no longer need to be moved.