Abstracts for the Conference on Grid Adaptivity in Computational PDEs, Edinburgh, July 96	Next
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A recursive quadrilateral unstructured mesh generator

J Sarrate A Huerta & N Montolí o

Departamento de Matemática Aplicada III
E.T.S. de Ingenieros de Caminos Canales y Puertos de Barcelona
Universitat Politècnica de Catalunya
Gran Capitán s/n, E-08034 Barcelona

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Abstract

In this paper a new quadrilateral two dimensional unstructured mesh generator is presented. The mesh generation algorithm is composed by three independent phases.

During the first one the domain is recursively splitted until only quadrilaterals of the desired size are left. An optimal line is chosen in every step minimizing a cost function defined as a linear combination of geometrical criteria. The rationale of using an objective function is that symmetry, right angles, as well as structured meshes and other properties can be favoured. In order to optimize the mesh generation algorithm, it has been implemented using a recursive technique. Some implementation strategies will be presented in the article.

In the second phase, the nodes are placed on the new generated lines using a linear interpolation of the element size. In order to adapt the element shape to each problem, the element size is defined by three parameters: an angle direction, the element size on it and the element size on its normal direction. These parameters can be specified on the base points of the contour or on the vertexes of a background mesh that covers the whole domain. The use of this background grid allows to concentrate elements in a particular area or in a prescribed direction.

Finally, a global smoothing is performed in order to adequate the discretization for the finite element computations. The proposed strategy which is based on geometric criteria allows to reduce in several orders of magnitude the element distortion.

Several mesh generation examples are presented. They range from standard academic cases to real engineering applications. They show the capability of the mesh generator to provide satisfactory meshes for finite element calculations. Finally, the mesh generator is used in the context of adaptative remeshing strategies based on error estimator.

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