八叉树网格到非结构混合网格的转换

Transformation From Octree Grid to Unstructured Hybrid Grid

在数值模拟中,非结构网格的优势是可以采用相同的数值格式统一处理任意复杂的计算区域,但在网格生成过程中难度大,并且不容易控制网格质量。树结构网格可以认为是介于结构网格和非结构网格之间的一种网格,目前已经有相对成熟的方法快速在复杂区域内生成二维四叉树网格和三维八叉树网格。在实际应用中,数值方法往往需要在连接协调的非结构网格上做离散,树结构网格中不同尺寸的网格之间连接不是协调的,在应用上会受到很多限制。文章实现了树结构网格到非结构混合网格的转换,这种转换在二维情况下就是将四叉树网格转换为非结构三角形和四边形的混合网格,三维情况下则将八叉树网格转换为非结构混合网格。这一转换过程的难点在于需要考虑数千种不同的八叉树单元,并给出能实现连接协调的非结构混合网格划分。可以出现的网格单元包括六面体、三棱柱、金字塔和四面体这4种不同情况。通过特别的分类,实现了程序的自动生成,这种程序自动生成技术一方面可以避免人工编写大量程序时的失误,另一方面也使得对数以千计的不同情况的处理成为可能。通过对几个简单网格的测试,对网格数据转换方法做了初步的验证。

Unstructured grids can be used in numerical simulation to deal with arbitrary complex computational regions in a unified scheme,but it is difficult to generate the grid and control the quality.Tree-structured grid can be considered as a kind of grid between structured grid and unstructured one.At present,there are relatively mature methods to quickly generate two-dimensional quadtree grid and three-dimensional octree grid in complex regions.In practical applications,discrete numerical methods often need to be applied on unstructured grids with coordinated connection,which is limited by tree-structured ones.In this paper,the transformation from tree-structured grid to unstructured hybrid grid was realized.In two-dimensional cases,the quadtree grid was transformed into unstructured triangle and quadrilateral hybrid grid,and in three-dimensional cases,the octree grid was transformed to unstructured hybrid grid.The difficulty of this transformation process is that thousands of different octree elements need to be considered,and an unstructured hybrid grid partition that can realize coordinated connection is given.The grid elements include four different cases:hexahedron,triangular prism,pyramid and tetrahedron.Through special classification,the automatic generation of programs was realized,which on the one hand avoids the error of writing a large number of programs manually,and on the other hand makes it possible to deal with thousands of different cases.Through testing several grids,the grid transformation method was preliminarily verified.