Font Size: a A A

Research On Two/Three Dimensional Unstructured Hybrid Mesh Deformation Methods

Posted on:2015-03-05Degree:DoctorType:Dissertation
Country:ChinaCandidate:T J LinFull Text:PDF
GTID:1220330467987190Subject:Engineering Mechanics
Abstract/Summary:PDF Full Text Request
In the field of engineering technology and nature, there are many flow problems with moving boundaries, such as fluid-structure interaction, multi-body separation, metal forming, fish swimming, birds flying and so on. The common characteristics of these problems are the strong interaction between the structures and fluids that causes highly unsteady, nonlinear flow phenomena. It is important for our industrial design departments to master the laws of this kind of unsteady flows. In the numerical simulation process to this type problem, a key technique is how to update the variational interior mesh with boundary moving, which named dynamic mesh. Dynamic mesh technique has become a hot subject in the interdisciplinary research field of computational fluid dynamics and computational solid mechanics. There are generally three ways to update unstructured meshes:mesh deformation, remeshing and combination of both. In this paper, we focus on the research of mesh deformation.Mesh deformation approaches are divided into three categories:pseudo-structural appr oach, partial differential equations and algebraic approach. Due to its simplicity, the spring analogy method belonging to the pseudo-structural class becomes one of the most popular mesh deformation techniques and is widely used in engineering and scientific research. However, when the domain boundaries undergo motions with relatively large amplitude, the spring method may fail. This paper mainly aims at overcoming the shortage of the spring method, including the following contents:1. Analysis the mechanism of spring analogy and study the improvement strategies. There are two major problems:first of all, the method is difficult to propagate boundary perturbation into the interior solution domain effectively. Secondly, it considers only the stretching forces along mesh edges and lacks control mechanisms for element collapse. In this paper, improvements are studied, including spring stiffness strategy and the ball-vertex method. By changing the stiffness under some strategy, e.g. boundary improvement, it can relieve the localization of deformation and enhance the deformation capacity of the mesh. The ball-vertex method introduces additional vertical linear springs which effectively confine each vertex within the polyhedral ball that encloses it. Numerical examples show that ball-vertex method can greatly improve the deformation capacity of the spring analogy method.2. A2D/3D unstructured hybrid dynamic mesh deformation method named as Vertex-Ball Spring Smoothing Method(VerBSS) is proposed. Although ball-vertex method is capable of dealing with practical engineering objects with large deformations, it is still rather time consuming as a large system of linear equilibrium equations has to be resolved. When a large number of nodes are involved, the computational efficiency may be pretty low. As an improvement to the original ball-vertex algorithm, the VerBSS method is proposed in this paper. Different from solving global equations, a "vertex-ball" system is built on each interior node. The mesh is smoothed layer by layer in an iterative manner and deformations of the boundary can propagate into the interior domain to achieve good results. According to the characteristic of the sub-system equations, an LDLT solver is introduced, which effectively reduces the computational cost. Furthermore, storing the data information in the nodal structure remarkably improves the space efficiency. Numerical examples have shown that the new method exhibits both robustness and computational efficiency and can be applied to complicated mesh topologies as well, not only to2D/3D dynamic mesh, but also to the hybrid dynamic mesh.3. An improved mesh deformation method based on Delaunay background grid morphing is proposed. When dealing with large movements, mesh quality decline sharply using the original method. To solve this shortage, we propose the improved strategy:by appending some assistant points in the initial graph, a new background graph is generated and a transition between the inner and outer boundaries is also formed. Then, the ball-vertex method which effectively avoids the occurrence of invalid elements is employed to move the new points. For the characteristic of the ball-vertex method, elements around the boundary have good shape retention. Numerical examples demonstrate that the improved method can effectively avoid the intersection problems and shows better performance in mesh quality. On the other hand, as the number of assistant points is small, the improved method keeps the efficiency as well.4. A weak coupling parallel method for large-scale unstructured mesh deformations is proposed. Based on VerBSS, we propose a weak coupling parallel method and have developed a universal, high performance computation module. Numerical examples in two and three dimensions have shown that parallel VerBSS takes full advantage of multiple processors, the efficiency is greatly improved. On the other hand, as the method is insensitive in geometric partition, the partition process is simplified. For example, a simple logical partition is enough for our algorithm. The parallel VerBSS is robust and capable of dealing with super large-scale dynamic mesh problems of complex geometries subject to large boundary deformations.
Keywords/Search Tags:Mesh deformation, Ball-vertex method, Mesh smoothing, Delaunay graph, Parallel scheme
PDF Full Text Request
Related items