Automatic Delaunay mesh generation method and physically-based mesh optimization method on two-dimensional regions

Abstract

Delaunay mesh generation method is a common method for unstructured mesh (or unstructured grid) generation. Delaunay mesh generation method can conveniently add new points to the existing mesh without remeshing the whole domain. However, the quality of the generated mesh is not high enough if compared with some mesh generation methods. To obtain high-quality mesh, this paper developed an automatic Delaunay mesh generation method and a physically-based mesh optimization method on two-dimensional regions. For the Delaunay mesh generation method, boundary-conforming problem was ensured by create nodes at centroid of mesh elements. The definition of node bubbles and element bubbles was provided to control local mesh coarseness and fineness automatically. For the physically-based mesh optimization method, the positions of boundary node bubbles are predefined, the positions of interior node bubbles are adjusted according to interbubble forces. Size of interior node bubbles is further adjusted according to the size of adjacent node bubbles. Several examples show that high-quality meshes are obtained after mesh optimization.