Complex Geometry
Automated hex meshing is by itself a very difficult art to master, as evidenced by the many decades of research that have and are currently going on in the field. We have successfully solved this problem using our STC based Spatial Matrix solver.
However there is yet another level of complexity above the STC called ComplexSTC that will make fully automatic hex meshing a mathematical impossibility, unless of course one has the algorithms to handle these cases. Such as those in the Spatial Matrix solver.
The upshot is that the STC solution to a complex geometric case is unique.
These complex cases are more common than not and usually appear in regions of interest both in terms of fluid flow and high stress crack propagation sites.
Examples besides those shown are; tire-road contact patch, the diffuser-tunnel start on an LMP car, the nose cone of a missile, gas-turbine combustion chamber diffuser.
This type of problem even though it looks very simple, is actually rather challenging to mesh with Hex cells, a challenge that is: to get a high quality result.
By placing a row of Hex cells around the edge, the cell in the middle is ideal at 90 degrees while the cell on the right is the best fit we can hope for. The problem is the cell on the left is too flat.
When we fix the left side the right side now is totally unacceptable.
This is the ideal solution. But as can be plainly seen the left and right side cells don't match up along the edge. This is the problem.
You may think this oblique intersection is a rare case, actually its more common than not.
These complex transitions are present on this engine nacelle, and for example; around the contact patch of a tyre and the road, at the wing root of aircraft, at the valve stem and inlet port of a straight port high performance engine and in turbo machinery diffusers.
This is the solution to the oblique pipe intersection example as generated by the Spatial Matrix solver and represented as a mesh with CheetahSTC.
The solution to a complex geometry model has a unique solution such that the STC solution is highly organized. The mesh shown here has the minimum number of valence transitions as seen by the 3 and 5 sided valence points. A minimal valence count solution is also referred to as the elegant solution.
This detail shows the only possible and feasible mesh solution for the inner corner. Once the edge angle gets tighter than this another solution is applied
And here we can see the desired mesh solution for the outer corner. The Cell3 for this example shall be available soon from the Cell3 Store along with many other complex geometry Cell3 models.