blockMesh is a commonly used utility for generating meshes in OpenFOAM. It reads a dictionary file, blockMeshDict, and stores the generated mesh in the directory constant.

The blockMeshDict file contains several sections, including vertices, edges, blocks, and boundary. These sections rely heavily on vertex indices, which can be difficult and error-prone to track.

A solution is to define the edges, blocks, and boundary block by block, where each block consists of 8 local vertices with a consistent ordering. While this simplifies dictionary definition, it introduces redundant vertices and results in disconnected blocks rather than a single continuous domain.

To address this issue, we introduce a global vertex list. By sorting and removing duplicated vertices, we construct a set of unique global vertices and establish a mapping between local and global vertex indices. This mapping enables the generation of a consistent and connected blockMeshDict.