An algorithm for decomposition of sub-domains and quadrilateral mesh generation with line constraints

Abstract

The technique for quadrilateral mesh generation on arbitrary 2-D domain has been quite mature; however, the existing methods and software can not directly deal with mesh generation with internal line constraints. In flood analysis and other analysis, the analysis models often contain a large number of constraint lines. In mesh generation, the sides of elements besides constraint lines must be attached to constraint lines, so that boundary conditions can be defined on these constraint lines. In this paper, a general method for automatic quadrilateral mesh generation with internal line constraints is presented. The mesh generation process is mainly divided into two stages, i.e. the automatic decomposition of sub-domains and quadrilateral mesh generation in each sub-domain. The sub-domains enclosed by constraint lines and boundaries are determined automatically with the proposal algorithm in this paper. Then nodes are generated on each edge of sub-domains based on mesh size requirements. By solving an integer linear programming problem, the number of nodes on each edge is adjusted automatically, so that the total number of boundary nodes in each sub-domain is even, satisfying the necessary condition for generating all-quadrilateral mesh. For free constraint lines in each sub-domain, the method of regarding constraint lines as holes with zero area is proposed, so that constraint lines can be treated as internal boundaries. The merging method of constraint lines and outer boundary is given, which can deal with all possible distribution of constraint lines and has generality. The examples of mesh generation with a large number of constraint lines are given to demonstrate the reliability of proposed method.