By Claudio M. Pita
Last month several Pointwise engineers attended the 24th International Meshing Roundtable (IMR) held in Austin, Texas. We brought two grids generated for two benchmark geometries provided by the IMR steering committee. The grids were made by Carolyn Woeber, Travis Carrigan, and myself. We were pleased to hear that the grids were recognized both for their technical merit and striking visuals - they had won the Meshing Contest award.
The goal of the Meshing Contest held at the 24th IMR this year was to generate a grid for one of the two provided geometries using any technique so long as the final mesh and file did not exceed 20 million cells and 1GB, respectively. Prompted by our passion for good grid generation challenges, we decided to mesh not just one, but both geometries. The IMR steering committee judged the entries based on the novelty of the approach, the complexity of the spatial discretization, the quality of the grids, the usability of the proposed solution, and finally the aesthetics of the poster displaying our work.
This year, the IMR steering committee provided two geometries: a CAD model of a Fender® Jazzmaster electric guitar and a 3-D scan of the human abdomen. This article describes the process by which the winning grids were generated using Pointwise.
One of the geometries provided by the IMR steering committee represented a Fender® Jazzmaster electric guitar, and it was provided in three different CAD formats: ACIS, Parasolid, and STEP. Although Pointwise is capable of importing each of these CAD formats, we ultimately used the STEP file. You can download the CAD files from the meshing contest website.
Upon importing the database surfaces, we noticed two things that needed to be addressed before generating the surface grids:
Another tool in our solid modeling feature suite called quilting was used to simplify the complex surface topology of the CAD model. While a model is a watertight representation of the geometry, quilts simplify the sometimes overly complex topology of the underlying geometry - they define logical meshing regions. Boundaries of quilts act as hard edges in the mesh and were used to define the hard edges of the geometry. With these geometry modifications, the model was complete and ready for the surface mesh.
With quilts defining the individual watertight meshing regions within a given model, surface meshing is as simple as specifying an average grid point spacing and clicking Domains on Database Entities in the toolbar. However, you can get more sophisticated and specify a maximum turning angle for adjacent surface elements, a maximum deviation from the underlying geometry, and a number of other parameters controlling the clustering of points within a domain. These parameters can be specified before creating a surface mesh from the Defaults panel or afterward from the Solve panel.
Typically, a uniform unstructured surface mesh for the model is generated using a grid point spacing that resolves some of its largest features. Next, the surface mesh is refined by adjusting connector distributions or unstructured domain attributes. This is exactly how the surface mesh for the guitar was generated. Because we cleaned up the geometry and defined an appropriate quilt topology beforehand, surface meshing was completed in just a couple of mouse clicks.
An advancing front algorithm was chosen to generate the triangular surface mesh for the guitar geometry. A benefit of the advancing front technique is its ability to capture curvature in a more regular fashion.
Since the primary structural component of an electric guitar is its neck, we elected to mesh the solid geometry for a structural analysis. An unstructured volume mesh, consisting of isotropic tetrahedra, was constructed from the resulting surface mesh and initialized using a modified Delaunay algorithm. The final mesh consists of 4.8 million isotropic tetrahedra.
Once the volume grid was initialized, it was prepared for export. This involved selecting a solver and then specifying the boundary conditions for the solver from the CAE menu. The IMR steering committee provided several options for export including the one we used: OpenFOAM®.
The second geometry provided by the IMR steering committee was called SPL Abdominal Atlas. It was provided by the Surgical Planning Laboratory at Brigham and Women's Hospital, Harvard Medical School. The atlas was derived from a computational tomography (CT) scan using a semi-automated image segmentation and three dimensional reconstruction technique. The CT scan was then converted into a triangulated stereolithography (STL) CAD formatted file prior to being imported into Pointwise. The original files in Nnrd and MRML formats can be downloaded from: https://www.spl.harvard.edu/publications/item/view/1918.
The focus of this meshing study was automation for a finite element analysis. A Glyph script was written to automatically do the following:
The geometry provided by the IMR steering committee consisted of 94 STL files containing 218 individual database surfaces. The imported surfaces were organized into different layers according to the body part they represented (Figure 3).
Once the geometric data was imported into Pointwise and organized into separate layers, then the database surfaces corresponding to each layer were each given a unique color. This step is crucial to visually distinguish the different body parts.
As mentioned before, the SPL Abdominal Atlas data was converted to a triangulated STL format prior to being imported into Pointwise. The original tessellation of each database surface was used to calculate an average spacing between grid points during surface mesh generation. Different views of the final surface grid are shown in Figures 4 and 5.
Although we generated a surface grid for every imported database surface, we elected to generate volume grids for a subset of the SPL Abdominal Atlas: two thoracic vertebrae and a single intervertebral disc. This decision was motivated by our desire to generate a volume grid suitable for basic intervertebral disc loading simulations. The final volume grid is shown in Figure 6.
Lastly, the script automatically generates a new Pointwise project file containing the organized database surfaces as well as surface and volume grids.
The IMR steering committee judged the entries based on their novelty, their complexity of spatial discretization, their grid quality, their proposed solution usability, and finally their poster's design aesthetic.
Once the final grids were complete, we struggled to figure out how to combine both of them into one aesthetically pleasing poster. The inspiration came to us from the fact that the 24th IMR overlapped by one day with the Austin City Limits music festival. Figure 7 shows the final result.
If you would like to generate your meshes using Pointwise request a free evaluation today.