A Generator of Tetrahedral Finite Elements for Multi-Material Objects or Fluids

Numerical Grid Generation in Computational Fluid Mechanics `88, Pineridge Press, pp.719-728, 1988

MESHING
RESEARCH
CORNER

in proceedings:
Numerical Grid Generation in Computational Fluid Mechanics '88, Edited by S. Sengupta, J. Hauser, P.R. Eiseman, J. F. Thompson.
Copyright 1988 Pineridge Press
ISBN 0-906674-68-9

Laboratoire d'ANALYSE NUMERIQUE Universite Pierre et Marie CURIE PARIS

INTRODUCTION
Today, the grid generation techniques may be divided into two classes. First, the structured technique takes advantage of hexahedral natural indexes and requires a decomposition of the object ( multi-material object or multi-fluid on the outside of an object) in hexahedral sub-blocks (1,2). The second technique, named un-structured or automated mesh generation, starts from either a set of points or a mesh of the object boundary (interfaces between materials and boundary) made of triangles or quadrangles and gives, either pentahedra or hexahedra by homothetic layers from the boundary, joined as well as possible, or tetrahedra by VORONOI's polyhedra and DELAUNAY's tesselation (3,4,5,6,7). These references describe a generator of tetrahedral mesh, named VDWHC (for VORONOI DELAUNAY WATSON HERMELINE CAVENDISH).The programming leads to solve five problems

• reduce the loop on only tetrahedra T which have a good probability for the circumsphere BCO to contain the new point P to add;
• choose a reliable test, unsensitive to the accumulated computer truncation error, to know if the point P is interior of B Cl') (6);
• prevent the creation of degenerate tetrahedra called 'slivers' by (6);
• add internal points, barycenters of too wide volume tetrahedra, from an initial wished distance of neightbouring vertices (5);
• respect the boundary and the interfaces between materials.