Research On Dual Mesh Deformation Based On Background Mesh And Vertex-Ball-Spring-Smoothing Method

The Moving Mesh Method is of great importance for various aspects relating to flow fields problems in Computational Fluid Dynamics(CFD)such as wing fluttering,multi-body separation,and fluid-structure interaction etc.The Moving Mesh Method mainly consists of mesh deformation,mesh reconstruction,and their combination.However,mesh reconstruction will change the topology of the original mesh,resulting in additional error in the flow field information transfer between the old and the new mesh,and affects the calculation accuracy as a result.Therefore,it is necessary to enhance the deformation capacity of the mesh as much as possible under the premise of ensuring the mesh quality and reducing the number of mesh reconstruction.These improvements are important to the subsequent numerical calculation.This dissertation mainly tackles the convergence of Vertex-Ball-Spring-Smoothing(VerBSS)method and the conformality of background mesh interpolation method.Moreover,some critical issues about advantages and shortcomings of these two methods,including computational efficiency,mesh quality,deformability and parallelization are studied as well.The following three topics are investigated:(1)A new BG-VerBSS mesh deformation method combining background mesh and VerBSS method is proposed.The slow convergence issue of the VerBSS method and the element intersection problem caused by the boundary inconsistency between the background mesh and the computational mesh are analyzed.The convergence of the BG-VerBSS method is accelerated by introducing the pre-deformation of the background mesh.The element intersection problem in the process of computational mesh deformation is circumvented by using smoothing method instead of interpolation method.We compared the relative error of the total nodal displacement with the iteration step during the iterative process and verify the acceleration effect of the proposed method.Numerical examples show that the number of iterations of BG-VerBSS in a single time step is decreased by 90% for two-dimensional problems and 70% for three-dimensional problems,and the deformation time of a single time step is decreased by 30% compared with VerBSS method.(2)Based on the BG-VerBSS method,a hybrid BG-RBF-VerBSS method is proposed by using Radial Basis Function method(RBF)for the deformation of the background mesh.The RBF method is used to pre-deform the coarse background mesh,and the deformation ability and mesh quality of the computational mesh are then improved by refining the background mesh.Three-dimensional examples demonstrate that the maximum deformation capacity of the method is improved by 23% ～ 52% compared with the greedy RBF method.In addition,the application of this method to hybrid meshes is also studied.All structured elements are decomposed into unstructured tetrahedral elements,and then the meshes of pure tetrahedral elements are deformed by the BG-RBF-VerBSS method.Finally,the proposed method is verified by numerical examples in which hybrid meshes are involved.(3)A partitioned parallel scheme for BG-RBF-VerBSS method based on Message Passing Interface(MPI)is proposed.The global mesh is partitioned,and the shared element layers are constructed on the boundaries of the adjacent partitions.The communication of the nodal displacements on the shared element layers of different sub-partitions is performed by MPI.The pre-deformation displacement of the background mesh is duplicated to the computational mesh of each sub-partition.This method mitigates the issue of convergence asynchrony between different partitions and reduces the iteration steps and communication time.Finally,the parallel efficiency of the method is verified by two-dimensional and threedimensional examples where the magnitudes of elements are of ten million.Two objectives have been achieved by combining the VerBSS method utilizing the background mesh: the computational efficiency and mesh quality of the VerBSS method are significantly improved by means of the pre-deformation of the background mesh,and the issues of unstable deformation in the background mesh method of direct interpolation are mitigated by using the VerBSS method to fix the uniformity point by point instead of the direct interpolation method;Partitioned parallelism is achieved in the VerBSS method by constructing a shared cell layer,and the computational asynchrony problem existing in the parallel process of the VerBSS method is alleviated by using the pre-deformation of the background mesh,which reduces the iteration steps and communication time and improves the acceleration ratio.Compared with other interpolation mesh deformation methods,the proposed methods have the advantages of higher efficiency,higher mesh quality,higher mesh deformation capacity,and better parallel efficiency.The proposed methods in this dissertation can be applied to super-large-scale mesh deformation problems.