Abstract

Nowadays large part of the time needed to perform a numerical simulation is spent
in preprocessing, especially in the geometry cleaning operations and mesh generation.
Furthermore, these operations are not easy to automatize because they
depend strongly on each geometrical model and they often need human interaction.
Many of these operations are needed to obtain a watertight geometry. Even
with a clean geometry, classical unstructured meshing methods (like Delaunay or
Advancing Front based ones) present critical weak points like the need of a given
quality in the boundary mesh or a relatively smooth size transition. These aspects
decrease their robustness and imply an extra e ort in order to reach the nal mesh.
Octree based meshers try to relax some of these requirements.
In the present work an octree based mesher for unstructured tetrahedra is presented.
The proposed mesher ensures the mesh generation avoiding most of the
geometry cleaning operations. It is based in the following steps: t an octree
onto the model, re ne it following given criteria, apply a tetrahedra pattern to
the octree cells and adapt the tetrahedra close to the contours in order to represent
accurately the boundary shape. An important and innovative aspect of the
proposed algorithm is it ensures the nal mesh preserves the topology and the
geometric features of the original model.
The method uses a Ray Casting based algorithm for the identi cation of the inner
and outer parts of the volumes involved in the model. This technique allows the
mesh generation of volumes even with non-watertight boundaries, and also opens
the use of the mesher for immersed methods only applying slight modi cations to
the algorithm.
The main advantages of the presented mesher are: robustness, no need for watertight
boundaries, independent on the contour mesh quality, preservation of geometrical
features (corners and ridges), original geometric topology guaranteed,
accurate representation of the contours, valid for immersed methods, and fast performance.
A lot of time in the preprocessing part of the numerical simulation is
saved thanks to the robustness of the mesher, which allows skipping most of the
geometry cleaning operations.
A shared memory parallel implementation of the algorithm has been done. The
e ectiveness of the algorithm and its implementation has been veri ed by some
validation examples.