Mesh Generation and Mesh Adaptation by Mesh Topology Optimization

2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999

MESHING
RESEARCH
CORNER

Ecole Superieure des Mines de Paris, CEMEF, umr CNRS 7635, BP 207, 06 904 Sophia Antipolis, FRANCE
Thierry.Coupez@cemef.cma.fr

Abstract
The work presented here is in continuation of the work of the author concerning the 3D remeshing (tetrahedral elements) in forming processes [1-4]. Some examples will be given of remeshing in 3D large deformation calculation using a Lagrangian descritption and a convected mesh and dealing with unilateral contact condition. These examples will show the robustness of a particular meshing method.

The theoretical aspect of this meshing method will be addressed. It is based on a new definition of a mesh which is introduced using a geometrical result based on a minimal volume principle. The equivalence between this definition and the classical one is proven. The mesh topology can be defined independently of the geometry and can be changed locally with respect to topological rules only. Then, i t is shown that non conform meshes can be optimized in order to recover a conform mesh, giving rise to a simple mesh generation method. The theoretical hypothesis behind the cut paste operation in a mesh topology are specified. The generic form of the global optimization algorithm will be presented; it is based on the combination of local improvement of the neighborhood of the nodes and the edges. The performance of the mesh generator will be discussed on complex examples providing the speed of performing a mesh without internal node and respecting exactly a given surface mesh. The mehing method is also designed to improve a mesh, by optimising a a mesh quality function and by inserting internal node.

The surface and the volume remeshing can be strongly coupled. For that purpose, a layer of virtual boundary elements is introduced which closes the mesh. The boundary faces can be treated as internal, the geometrical constraint being to maintain a null volume to the virtual elements.

A mesh size map can be introduced directly in the shape factor of elements. The mesh optimization of the modified shape factor provides implicitly the adapted mesh. Finally the adaptation cycle is presented, which consists in computing a mesh size map on the current mesh, to adapt the mesh, to compute again the mesh sie map and to adapt again until a convergence state is reached. Examples in static and dynamic adaptation will be given.

References

[1] T.Coupez. 'A mesh improvement method for 3d automatic remeshing', In N.P. Weatherill et al., editor, Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, pages 615--626. Pineridge Press, 1994.

[2] T.Coupez, 'Automatic remeshing in three-dimensional moving mesh finite element analysis of industrial forming' in Shan-Fu Shen et al., editor, Numerical Methods in Industrial Forming Processes - NUMIFORM 95,pp 407--412. A.A. Balkema, 1995.

[3] T.Coupez, 'Parallel adaptive remeshing in 3d moving mesh finite element', In B.K. Soni et al., editor, Numerical Grid Generation in Computational Field Simulations, volume 1, pp 783--792. Mississipi State University, 1996.

[4] T.Coupez, 'Adaptive meshing for forming processes', In M. Cross et al, editor, Numerical Grid Generation in Computational Field Simulation. U. of Greenwich, Mississipi State University, July 1998.