Transition Layers in Mesh Control
While practising for the upcoming Simulation Premium training class this week that I am going to teach, I came across an instance where I wanted to control the number of layers for the growth of mesh size. Prior to 2009, the Mesh Control utility in Simulation permitted the user to specify the number of layers to grow from the local element size to the global element size. This functionality is gone in 2009. That confused me as much as some of the attendees at the COSSUG meeting two weeks ago in Columbus, OH.
Well, the solution is tricky to get to, but is available in 2009!!
Apparently, the two options available now are the desired local element size, and a ratio called a/b. The ratio was defined previously as the desired Aspect Ratio (or a measure of skewedness of the elements). In 2009, the definition has been re-written as the ratio of the element size in one layer to the element size in the preceding layer.
Now, that got me thinking about how to back-calculate and hence control the number of layers. So here is the solution:
The general expression that dictates mesh sizes can be stated as:
Here is an example:
Suppose I want the local size to be 0.2mm and the global size to be 0.3456mm, and the number of layers to be 3. I can calculate the a/b value by substituting these numbers into the above equation. I end up with a value of 1.2, which would yield the desired result in the mesh. If I want the number of layers to be 10, I can re-calculate the equation, and the new a/b value is 1.056.
As a generalized observed rule, the smaller the a/b value, the slower the growth rate.
So pull out those calculators, and start punching away!! The functionality is still there.