A new mesh deformation method based on disk relaxation algorithm with pre-displacement and post-smoothing

Mesh deformation is crucial to the accuracy and efficiency of the numerical simulations involving moving boundaries. In this paper, the disk relaxation algorithm and background mesh are applied to develop a new mesh deformation method. The disk relaxation algorithm rearranges the nodes in the mesh by repulsive and attractive interactions to preserve high mesh quality. With the help of background mesh, the computational region is divided into layers to transfer the boundary deformation uniformly and effectively in the pre-displacement procedure. We further introduce the post-smoothing procedure to avoid the negative volume of elements. Numerical applications including the rotation of airfoil, rotation and translation of rectangle, relative motion of multi-body, and complex boundary with irregular deformation are carried out. The results demonstrate that the new method generates the deformed mesh with high quality even in large deformations, especially concerning the boundary meshes. Comparisons with previous methods show that the deformation capability and efficiency of the new method are better than the widely used semi-torsional spring analogy, and the mesh quality of the deformed mesh obtained is superior to that of the spring method, as well as some new approaches presented recently when they undergo the same deformation in the cases.