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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 80
Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 22

Anisotropic Quadrilateral Meshing: An Indirect Approach

D. Merhof+, R. Grosso+ and U. Tremel*

+Computer Graphics Group, University of Erlangen, Germany
*EADS Military Aircraft, Flight Physics / Numerical Simulation, Munich, Germany

Full Bibliographic Reference for this paper
D. Merhof, R. Grosso, U. Tremel, "Anisotropic Quadrilateral Meshing: An Indirect Approach", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Fourth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 22, 2004. doi:10.4203/ccp.80.22
Keywords: mesh generation, surface mesh, anisotropy, quadrilateral, unstructured meshes, advancing front approach.

In this paper a new indirect approach is presented for the generation of anisotropic quadrilateral meshes.

The generation of surface meshes has been a widely explored topic in the field of Computational Fluid Dynamics. Algorithms for the generation of triangular surface meshes are currently in wide use. Recently, attention has also been given to the generation of quadrilateral surface meshes [1,2]. The reason is that for a given node density, quadrilateral meshes contain only half as much elements as triangular meshes. The saving of elements continues when a volume mesh is generated using an advancing front method. If quadrilateral meshes serve as starting point for the volume mesh creation, the resulting volume meshes provide the same quality (node density) but comprise a significantly lower number of volume elements, which is a highly desirable characteristic. A second possibility to reduce the number of surface elements, and as a result the number of volume elements, is to introduce anisotropic elements. Anisotropic meshes have the property that the density of nodes is direction dependent. Several previous endeavours have been made for developing algorithms to gain anisotropic triangular meshes [3,4].

The goal of this paper is to extend the benefits of unstructured quadrilateral meshes by including anisotropic elements that contribute to the desired reduction of elements and nodes. This approach provides the possibility to generate application optimised meshes with a minimum number of elements. The algorithm presented in this paper has the following properties:

  • The algorithm works on high resolution triangular meshes. An approach to local surface approximations enables the algorithm to handle triangular surface meshes not only in 2D but also in 3D.

  • Anisotropic quadrilaterals are generated along an anisotropy source which has to be specified by the user, e.g. a line source consisting of all mesh edges defining the leading edge of an air plane wing

  • Several iterations of quadrilateral creation and anisotropic quadrilateral merging are performed to obtain anisotropic elements along the source. With growing distance to the source the anisotropy decreases according to the mesh size of the background triangular mesh.

The results presented in this paper show that the reduction of elements by using anisotropic quadrilaterals generated with our algorithm is remarkable. The algorithm is thus capable to generate application optimised meshes so that processing times for fluid flow computations are reduced.

T.D. Blacker, M.B. Stephenson, "Paving: A new Approach to Automated Quadrilateral Mesh Generation", Int. J. Numer. Meth. Engng., 32, 811-847, 1991. doi:10.1002/nme.1620320410
S.J. Owen, M.L. Staten, S.A. Canann, S. Saigal, "Q-MORPH: an indirect approach to advancing front quad meshing", Int. J. for Numer. Meth. Eng., 44, 1317-1340, 1999. doi:10.1002/(SICI)1097-0207(19990330)44:9<1317::AID-NME532>3.0.CO;2-N
F.J. Bossen, P.S., "A Pliant Method for Anisotropic Mesh Generation", In Proc. of 5th Int. Meshing Roundtable, 63-74, 1996.
K. Shimada, A. Yamada, T. Itoh, "Anisotropic Triangular Meshing of Parametric Surfaces via Close Packing of Ellipsoidal Bubbles", In Proc. of 6th Int. Meshing Roundtable, 375-390, 1997.

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