Study On Quadrilateral Mesh Generation Based On Submapping

Structured grids have advantages of high grid quality, short generating time and simple data structure. Thus structured grids are still widely used in numerical simulations which need aligned grid cells, for instance, the flood Analysis numerical simulation usually require the trend of meshes are consistent with the direction of the water flow, thus, structured mesh is the best choice. Mapping is now the most widely used method to generate structured meshes. This method generates meshes by a mapping transformation between physical area and calculation area. But the mapping method can only used in quadrilateral area. For complex areas, it needs to manually decompose the area into several quadrilateral subareas, and then use mapping method to generate meshes in every subareas, this makes the generation of structured meshes in complex areas needs human interaction and is hard to achieve automation of mesh generation. Therefore, research on generating structured meshes of complex area automatically and improve the efficiency of mesh generation, has certain theoretical significance and practical application value.This paper proposes a method which can automatically generate structured quadrilateral mesh of complex areas—submapping. The method decomposes geometric region into several quadrilateral subareas, and by solving an integer linear programming problem to keep the compatibility between each subarea, finally using transfinite interpolation method for each subarea to generate structured quadrilateral meshes.The procedure of generating structured mesh based on submapping includes: vertex classification, boundary classification, boundary node number distribution, boundary discretization, geometry decomposition, and subarea meshing. This paper divides the vertices of physical area into four categories, the angles in the corresponding calculation area are integer numbers of π/2. In order to satisfy the necessary condition that the sum of all Angles in the calculation area is equal to 2π, this paper proposes an optimized method which uses integer linear programming to adjust the vertex types, meet the necessary conditions for structured mesh generation. In order to ensure the compatibility between each subarea, all node numbers in+1 direction must be equal to all node numbers in -I direction, all node numbers in+J direction must be equal to all node numbers in -J direction, this paper proposes an optimized method which uses integer linear programming to adjust the node numbers in each edge, meets the requirement of the mesh compatibility. For decomposition of geometry, this paper proposes a recursive decomposition method, the area is decomposed into a series of quadrilateral subareas. Based on subarea mapping method, this paper develops a structured quadrilateral mesh generation program which has been applied in two-dimensional analysis of flood.