Quadrilateral surface mesh generation with improved quality by combination of triangles

Quadrilateral mesh is preferred in numerical simulation compared with triangular mesh, but high-quality and robust quadrilateral mesh generation for complex geometries remains a challenging problem. In this study, an enhanced indirect method by the combination of triangles is proposed for the generation of high-quality quadrilateral mesh. It takes a triangular mesh as the input, and except that the number of elements needs to be even, the triangular mesh can be generated by the commonly used AFT method or Delaunay method. To ensure the quality of the combined quads, a local-global triangular remeshing procedure is conducted first, and size gradation and vertex valence are focused in this step. Then, the well-known Blossom algorithm is used to find the perfect matching triangles for combination. Finally, in order to reduce the number of unnecessary singularities, a connectivity optimization procedure is introduced to replace the irregular elements in local regions with regular elements and thus improve the overall quality of the combined quads. Numerical experiments on meshes in both 2D and 3D cases are presented to demonstrate the effectiveness of the proposed method.