| The technique of adjusting the computational grid according to the movement or deformation of the boundary is called the dynamic mesh technique.Dynamic mesh techniques are widely used in mechanical engineering problems such as fluid-structure interaction.Dynamic mesh techniques can be divided into mesh reconstruction methods and mesh deformation methods.The mesh reconstruction methods re-generate the mesh based on the new boundary in the calculation area,which is costly and increases the dissipation error.In the field of mesh deformation,there is no mesh deformation method that has both excellent mesh deformation ability and computational efficiency and strong robustness.Improving existing mesh deformation methods or proposing new mesh deformation methods are very valuable research directions.In the mesh deformation method,the initially generated mesh significantly affects the subsequent mesh deformation process.The existing unstructured grid deformation methods include front-advance method,octree method and Delaunay grid generation method.There is still a lack of automatic hexahedral mesh generation methods,so the research on mesh generation methods is of great significance.This paper investigates the existing mesh deformation methods.The characteristics of deformability,time cost and robustness of each mesh deformation method are summarized and evaluated.At the same time,this article investigates the unstructured grid generation methods,evaluates and compares the pros and cons of the three existing mainstream methods.The dynamic mesh method based on the sphere relaxation algorithm(sphere relaxation method)can generate higher-quality boundary mesh and achieve larger deformation than the traditional spring method even for shape-complex boundaries and large boundary deformations.However,the time efficiency of this method still has room for improvement.In this work,we present a double-grid strategy which introduces a coarse mesh besides the computational mesh(fine mesh).The sphere relaxation algorithm is applied to deform the coarse mesh and transfer the boundary displacement to the entire region which replace the predeformation step in the sphere relaxation method.Then,the double-grid mapping is carried out to map the displacements of the coarse mesh into the computational mesh.Examples show that computational time is reduced by this improvement.We also study the effects of the node number ratio(coarse mesh/fine mesh)on the computational efficiency,deformation ability and mesh quality.Numerical examples indicate that the optimal node number ratio is about0.5 for the best efficiency.This paper analyzes and compares three typical mesh deformation methods: spring method,RBF method and elastic method.The calculation example shows that the elastic method has the strongest mesh deformation ability,and its biggest deformation can reach 12 times of RBF method.However,the time cost of the dynamic mesh elastic method is too high,and there is a lot of room for improvement.This paper introduces the improvement of the greedy point selection strategy of RBF method,and introduces the greedy point selection strategy into the elastic method.Based on the greedy method,this paper reduces the boundary nodes and regenerate a sparser grid,which is called coarse mesh.The calculation examples show that the improvement can effectively improve the deformation efficiency of the elastic method,and the reduction of mesh quality is within an acceptable range.Research shows that the improved method has the best performance when the ratio of the number of points is 0.5.In this paper,packing algorithms are introduced into the field of mesh generation,and the mesh generation problem is transformed into a packing system problem with 100%packing density.This article proposes an adaptive Monte-Carlo algorithm suitable for fixed boundaries.A particle deformation method based on nodal attraction and spring force is further proposed to ensure that the packing density reaches 100% under complex boundary conditions.The results of calculation examples show that this method can be effectively applied to the generation of hybrid meshes. |
