Prev: 7.1.1 Surface Extraction

7.1.2 Meshing

The meshing tool uses a modified advancing front algorithm to generate a three-dimensional unstructured tetrahedral mesh of the simulation domain [16][17]. Starting with the initial surface given as list of triangles, additional information such as the size of the reactor region above the feature and additional points within this region are necessary. The meshing tool provides three different strategies for the generation of additional point clouds. The first one uses the leafs of the octree, built up internally by the meshing tool in order to store the points of the initial surface for the scattering of additional mesh points. A second method applies an advancing front technique for the placement of mesh points suitable to produce boundary-fitted meshes. Finally tensor product point clouds or random point distributions adapted to inhomogeneous density requirements can be added.

Figure 7.3: Propagation of the advancing front used for the three-dimensional meshing of the gas space above the feature.

For the demonstration of the meshing procedure, a uniformly distributed tensor product point cloud was inserted into the simulation domain and the meshing process was interrupted several times. At any time the resulting snapshot is a valid mesh of part of the domain. From top left to bottom right, Fig. 7.3 plays back the propagation of the advancing front. The initial surface is given in the top left figure. The next figure shows that the front has already started to propagate trough the simulation domain incorporating the mesh points of the tensor product grid from the interior. The ``gaps'' which can be observed beginning with the 3rd picture allow to look trough the structure and indicate that the valid mesh in some parts already connects the front side boundary with the backside boundary of the simulation domain. With the propagating front, the valid mesh spreads throughout the domain until all small cavities remaining in the corners of the domain (see bottommost row in Fig. 7.3) are connected to the final three-dimensional mesh of the structure.

Figure 7.4: Cross-section through the three-dimensional mesh showing the tetrahedra connecting adaptive ortho style point clouds in the interior with the boundary triangles generated by the surface extraction. Shading indicates the normalized ${\rm WF\hspace*{-0.2ex}_6}$ distribution.

For the high-pressure CVD simulation an adaptively resolved grid was achieved by specifying vertically stacked tensor product point clouds with different horizontal and vertical grid spacings. A cross-section of such a mesh can be seen in Fig. 7.4, a three-dimensional view thereof is given in the summarizing flowchart in Fig. 7.5(c).

Prev: 7.1.1 Surface Extraction