Boundary treatment for 2D elliptic mesh generation in complex geometries

This paper presents a boundary treatment method for 2D elliptic mesh generation in complex geometries. Corresponding to Neumann–Dirichlet boundary conditions (sliding boundary conditions), the proposed method aims at achieving orthogonal and smooth nodal distribution along irregular boundaries. In this method, a three-lined auxiliary mesh is constructed which is composed of the boundary line, an auxiliary line generated on its inner side, and the reflection line of this auxiliary line. The movements of the boundary nodes are determined by solving this auxiliary mesh. The boundary nodes are further corrected and adjusted by a second-order parabolic interpolation method and a weighting parameter depending on the curvature of the boundary. The proposed method was demonstrated through examples, and applied to field cases with complex geometries. It has been shown that this method is stable and effective in producing high quality meshes.