Quadrilateral Meshing with Anisotropy and Directionality Control via Close Packing of Rectangular Cells

A new technique for automatically generating anisotropic quadrilateral meshes is presented in this paper. The inputs are (1) a 2D geometric domain and (2) a desired anisotropy – defined as a metric tensor over the domain – specifying mesh sizing in two independent directions. Node locations are obtained by closely packing rectangles in accordance with the inputs. The centers of the rectangles, or node, are then connected using anisotropic Delaunay triangulation that takes into account the desired anisotropy. The obtained triangular mesh is converted into a quadrilateral mesh using mesh conversion templates. The novelty of the method is that closely packed rectangles resemble a pattern of Voronoi polygons corresponding to a well-shaped quadrilateral mesh. The result is a high quality mesh that conforms well to the input. As a sample application, this method was used to generate a mesh to solve a steady state heat transfer problem.