Abstract
Certain classes of problems result in solution fields of which the characteristic length scales vary with the orientation. Often the orientation of these length scales is related to the orientation of the boundaries. Such solution fields can be captured by the finite element method, using a mesh that is refined in the direction of the short length scales and coarse in the other directions. These meshes contain elements with high aspect ratios in a predefined pattern.
The mesh generator presented here can render triangles with high aspect ratios through a paving algorithm. The paving algorithm that is employed applies both triangles and quadrilaterals, combining the advantages of both to render a qualitatively good, oriented triangular mesh, with a concentration of elements in the direction where the internal length scales of the solution field are the shortest.
The mesh generator produces triangles with one (almost) orthogonal corner. When low aspect ratio triangles are generated, these are well suited for conversion to quadrilateral elements. Test results indicate that quadrilateral meshes converted from the mesh generator introduced here have a considerably better quality than those converted from several other triangular mesh generators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Zheng, Y., Lewis, R. W., Gethin, D. T. (1996) Three-dimensional unstructured mesh generation: Part 1. Fundamental aspects of triangulation and points creation, Comput. Methods Appl. Mech. Engineering, 134; 249–268
Blacker, T. D., Stephenson, M. B. (1991) Paving: a new approach to automated quadrilateral mesh generation, Int. J. Numer. Methods Engineering, 32; 811–847
Löhner, R. (1993) Matching semi-structured and unstructured grids for Navier-Stokes calculations, AIAA 93-3348-CP, 555–564
Löhner, R. (1996) Progress in grid generation via the advancing front technique, Engineering with computers, 12; 186–210
Segal, G. (1997) Sepran User Manual/Programmer's Guide, Ingenieursbureau SEPRA. Leidschendam, The Netherlands
Zhu, J. Z., Zienkiewicz, O. C., Hinton, E., Wu, J. (1991) A new approach to the development of automatic quadrilateral mesh generation, Int. J. Numer. Methods Engineering, 32; 849–866
Lee, C. K., Lo, S. H. (1994) A new scheme for the generation of a graded quadrilateral mesh. Computers Structures, 52(5);847–857
Cheng, B., Topping, B. H. V. (1997) A simple and efficient method for converting triangular meshes to mixed meshes in parallel mesh generation, in: Advances in computational mechanics with parallel and distributed processing, Civil-Comp Press, Edinburgh, 15–23
Johnston, B. P., Sullivan, J. M., Kwasnik, A. (1991) Automatic conversion of triangular finite element meshes to quadrilateral elements, Int. J. Numer. Methods Engineering 31; 67–84
Rank, E., Schweingruber, M., Sommer, M. (1993) Adaptive mesh generation and transformation of triangular to quadrilateral meshes. Com. Numer. Methods Engineering, 9:121–129
Shewchuk, J. R. (1996) Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. First Workshop on Applied Computational Geometry, 124–133. Association for Computing Machinery. (Http://www.cs.cmu.edu/~quake/triangle.html.)
Schoofs, A. J. G., van Breukeling, L. H. Th. M., Sluiter, M. L. C. (1979) A general two-dimensional mesh generator, Advances in Engineering Software, 1(3); 131–136
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van Rens, B.J.E., Brokken, D., Brekelmans, W.A.M. et al. A two-dimensional paving mesh generator for triangles with controllable aspect ratio and quadrilaterals with high quality. Engineering with Computers 14, 248–259 (1998). https://doi.org/10.1007/BF01215978
Issue Date:
DOI: https://doi.org/10.1007/BF01215978