Square Packing ... for Quadrilateral Mesh Generation

Abstract This page shows a method for generating well-shaped and well-aligned quadrilateral meshes for numerical simulations, and so on. The method assumes virtual square particles, which have attractive and repulsive forces. This method first scatters the particle inside a given domain, and calculates the equation between the forces of them. The location of the tightly packed particles is finally obtained, and a quadrilateral mesh is obtained by connecting the centers of the particles. Background This project has been already proposed a quadrilateral meshing scheme, that first automatically generates triangular meshes by the bubble mesh method, and then automatically converts the triangular meshes into quadrilateral meshes. However, it does not always generate well-shaped quadrilateral meshes, because it difficult to generate regular quadrilateral element by the coupling of regular triangular elements generated by the bubble mesh method. This project therefore considered of developing the new method to obtain the adequate location of mesh-nodes for quadrilateral meshing, as an extension of the bubble mesh method. Principle The basic idea of the square packing method is that packs square particles, instead of packing circle particles in the bubble mesh method. The above figures (a)(b) show the tightly packed bubbles, and regular triangular elements generated by connecting centers of the packed bubbles. Replacing bubbles by squares, and connecting centers of squares, regular quadrilateral elements can be generated as shown in the above figures (c)(d). The above figures show the distribution of repulsive forces between a circle particle of the bubble mesh method, and a square particle of the square packing method. As shown in the figures, the square packing method assumes the maximum repulsive force at the center of a square particle, and local-maximum repulsive forces at the four vertices of the particle. By the combination of these forces, an equivalent force of curve of the particle figures nearly a square. Example The above figures show the example of the input data for the square packing method. The left figure shows a scalar function that represents the distribution of sizes of square particles. The right figure shows a vector function that represents the directionality of the particles. The square packing method flexibly generates quadrilateral meshes as users desire, by controlling the two functions. The above figures show the tightly packed particles, and a quadrilateral mesh generated by connecting centers of the particles. This page also shows the Animation of the process of packing square particles (324KB). The above result shows that the quadrilateral mesh is well-shaped, and sizes and directionality are well-controlled. Here the advantages of the square packing method can be summarized as follows: Generation of regular quadrilateral elements. Flexible control of sizes of elements by using a scalar function. Flexible control of alignment directionality by using a vector function. Especially we would like to emphasize that control of alignment directionality is very important for numerical simulations, however, conventional quadrilateral meshing methods cannot control it flexibly. We think that the capability of directionality control in the square packing method is a great advantage. To the top page of meshing project

Last modified 30 Sep 1999