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.

Delaunay网格生成方法是非结构化网格（或非结构化网格）生成的常用方法。Delaunay网格生成方法可以在不重新划分整个域的情况下方便地向现有网格添加新点。但是，与某些网格生成方法相比，生成的网格的质量不够高。为了获得高质量的网格，本文开发了一种自动的Delaunay网格生成方法和一种基于物理的二维区域网格优化方法。对于Delaunay网格生成方法，通过在网格单元质心处创建节点来确保边界符合问题。提供了节点气泡和元素气泡的定义，以自动控制局部网格的粗糙度和细度。对于基于物理的网格优化方法，预定义边界节点气泡的位置，根据气泡间力调整内部节点气泡的位置。内部节点气泡的大小根据相邻节点气泡的大小进一步调整。几个示例表明，在网格优化后可获得高质量的网格。