Research Of Complex Boundary Adaptive Quadrilateral Mesh Generation Based On Quadtree Mesh

Mesh generation is indispensable to the pre-processing section of Finite Element Analysis (FEM). Only when the target domain is meshed, can it be solved by FEM method. Generally speaking, typical body-fitted grid method is unfit for adaptive mesh generation of complex boundaries. As a typical non-body-fitted grid method, Cartesian grid is becoming more and more popular in complex boundary mesh generation field.At the moment, Cartesian cut-cell method merely limits to single-edge cutting when dealing with boundary cuttings. Another limitation is that it handles cut cells mainly through cell merging which will generate hanging nodes. And hanging nodes cannot be used by FEM.Aiming at those problems, this article makes deep research on the Cartesian cut-cell method. The paper firstly revises one of the termination conditions of balanced quadtree meshing as dual-edge cutting. In order to make it convenient for analysis and judging, relative position of two segments and mesh types are classified in detail and correlative concepts are declared or defined. On this basis, algorithms of distinguishing relative position of two segments and grid inside-outside judging are proposed separately. Creatively, grid diagonal line standard intersection judge method is put forward to judge whether a grid is cut only by domain edge.Secondly, this article researches deeply on the law and characteristics of hanging nodes and presents the concepts of hanging node loops and hanging node chains to handle hanging nodes in the initial meshes. In this research process, templates of handling hanging nodes on the loops and chains are given. Node movement is implemented after hanging node processing for the purpose of eliminating tiny grids and hanging nodes that are domain vertexes.Thirdly, in boundary cutting section, the document deliberates many edge-cut circumstances and sums up the regular edge-cut pattern. Single-edge cutting and domain vertex cutting, two of the grid cut patterns, are chosen to be the basic edge-cut patterns. And the other cut patterns can be seen as the combination of the two basic edge-cut patterns.This article efficaciously solves the cut grids that are cut by under-three domain edges through the two basic edge-cut patterns and obtains eight kinds of cut cells. Then, quadrangulating templates are given according to each kind of cut cells. Using those templates, cut cells can be quadified without introducing hanging nodes. Some examples are also given to validate the common templates.At last, meshes are smoothed by Laplace method and the smoothed meshes are then be applied to simulate Karman vortex street and backward-facing step flow with the purpose of illustrating the feasibility and efficacy of the proposed meshing method.