mesh quality
 

Dear all,
I need to determine the quality of a 2D structured FEM mesh. I calculated the minimum value of the Jacobean and surface area for each cell, and both are positive. I could also compute a scaled version of the aforementioned variables (i.e., ratio of Jacobean with minimum edge).

Could someone give me some criteria of what qualifies as a good mesh? Is there a reference that I could read?

Thank you

Vasilis:

Because you wrote "structured" mesh, I'll assume you have a 2D mapped mesh of linear quads.

One measure to consider would be the cell to cell variation in area. Another interesting quality metric would be the "smoothness" of the grid lines in the i and j directions. (For smoothness you can compute something like the angle change in the line from cell to cell.)

There are many other metrics you could compute with as many references supporting their use. What matters is what's important to your flow solver. That should be documented in their user manual.

Best Regards

Hi jchawner,

The entire code is written by me. I calculated the ratio of the minimum value of the Jacobian at the Gauss points for each cell over the area of that cell. I found that this ratio is equal to 0.25, for the majority of the elements (more than 90%), but it could also be as small as 0.033. What does this tell me about the mesh quality? In a paper, I found that this ratio should be between 0 and 1. If it is equal to 0, the element is badly shaped.

Could I argue that I have a few skewed elements, but, overall, I have a good quality mesh?

Like most things in mesh quality the answer is "it depends."

It depends on whether the cell with ratio = 0.033 is located where something interesting is happening in the flow.

It depends on whether your flow solver is sensitive to this ratio. You wrote that you read a paper about acceptable values for the ratio, but maybe that pertains to the author's solver, not yours. For example, Fluent uses some very distinct methods for computing cell skewness - but those may not pertain to STAR-CCM+.

Let me answer your question with another question. If all the elements in your mesh had positive area except for one that had negative area and it prevented your solver from running, could you argue that overall you have a good quality mesh?

All that matters in mesh generation is creating a discretization that allows the solver to run and converge to an accurate solution.

If this is indeed the case, then I do have a good mesh. The solution has converged (same solution for two different meshes), and there is an excellent agreement of the numerical solution with the experimental data.

The code stops if it finds a cell with a negative Jacobian.

I was asked to prove that my code produces a good quality mesh. I believe that the the fact that more than 99% of the elements have a scaled Jacobian in the range of [0.2-0.25] is an indication of a good quality mesh.

jchawner, thank you for your help.