Scaled Jacobian Issues


#1

Hi all!

Lately I have been working on a project where I needed to calculate the wind load over a loudspeaker system (below you can see the geometry of it).

Later, the effects of this wind load over the frame structure is to be studied. As it was my first “big” simulation I was only looking for a “pretty looking” mesh in order to run a fast simulation to get some raw numbers for a first structural simulation. I didn’t check the quality metrics of the mesh till now… And this is what I found!

Surface Element Quality Metrics
Area                     Max: 0.00163929, Min: 2.14471e-09, Avg: 2.9381780352086442e-05
Aspect ratio             Max: 138.588, Min: 1, Avg: 1.4984095575650402
Skew                     Max: 0.999888, Min: 0, Avg: 0.04134366074637352
Scaled Jacobian          Max: 1, Min: -0.946908, Avg: 0.9845244350433492
Condition                Max: 5e+29, Min: 1, Avg: 5.770574225034172e+26
Volume Element Quality Metrics
Volume                   Max: 6.55869e-05, Min: 1.77457e-10, Avg: 9.90752e-07
Skew                     Max: 0.994358, Min: 0, Avg: 0.0824641
**Scaled Jacobian          Max: 1, **Min: -0.940889, Avg: 0.951213

If you look at the average Scaled Jacobian, it looks very good! nothing to say about it. However, if you look at the minimum value you may get a shock!

Whats the meaning of a negative Scaled Jacobian? How can it affect the accuracy of the results? Do I need to remesh the case?

Below I attach some pictures so as you can get a better insight to my problem and give me some valuable feedback.

Scaled Jacobian in a clipped mesh

Scaled Jacobian in a clipped mesh (detail)

Scaled Jacobian (front)

Scaled Jacobian (negative values only)

Scaled Jacobian (values <-0.01 only)

After studying these pictures I have some questions.

  1. First, most of the green cells (Jacobian=0) shown in the first pictures are the cells belonging to the boundaries of refinement areas, as it can be noticed in the picture below

Is it normal that the cells that delimit refinement levels have a 0 Scaled Jacobian? Is it bad?

  1. Second, what implications have working with negative values for Scaled Jacobian? Should I avoid it? I can imagine the answer…

  2. If so, what should I do in order to prevent from creating negative Scaled Jacobian cells while meshing?

I am really concerned about it and I would like to get some feedback from experienced users that can help me to improve, if needed, my mesh strategy for this case.

I’m really looking forward to some interesting reply!

Best regards,

Alex Roqué


#2

Hi Alex!

Nice to see you again. I notice you’ve started on the full loudspeaker simulation! Now onto your question which I hope I can adequately answer.

After a brief google search to read up about the scaled Jacobian cells its basically a quality indication of sorts. This article explains the Jacobian cells in general and usually its for FEA from other places I’ve looked through like this. So, onto the questions which I will try to answer as best as I can. Forewarning though, this is still rather new to me and I’ll explain why I don’t really pay that much attention to this at the moment.

If you look at the first link I provided, it basically means that the cell is practically inverted. How it affects the accuracy of the results is highly subjective. You would have some deviation in your results for sure but by how much? Could be anywhere from 0.0000001% to a complete error. Do you need to re-mesh? No I don’t think so, again I’ll explain why later.

A Jacobian of less than 1 is possible. Is it bad? Typically yes. A fatal error? Subjective, it may or may kill your results.

The obvious answer would be either an error or a deviation in the results by a certain margin. Again, what that margin is, is very subjective based on your case. Like any poor cell quality, you should avoided as much as possible unless it produces a fatal error of sorts then you will need to avoid it completely (which may or may not possible for complex geometries).

While the individual Hex-Parametric controls are sure to help in negating this, optimizing those numbers might be tricky. Will need to some read up on each individual option. In the meantime, ensuring your geometry is as simple as possible, clean and watertight usually gives you the biggest gains in terms of approaching ideal mesh quality.

Now, why do I not really look into ensuring Jacobian cells are not negative? Because my results do match. If your case does have some form of validation be it experimental or empirical, ensuring the results are compared against those values is highly critical to ensure your mesh and subsequently simulation is producing realistic results. You can also perform a mesh convergence study to observe how mesh quality affects results sensitivity hence why I mentioned you don’t need to re-mesh, just simulate this and check your results. This is something I would recommend anyone to do.

It is important to note while mesh quality checks are good and all, for complex geometries this may not always or even ever be satisfied. Rather, look at your results and deduce the sources of error from there. Understand what is deemed an acceptable result deviation and where those errors come from. This way you’re able to produce results from a project quicker as you can understand and isolate issues.

Hope this helps. If I do make any mistake feel free to correct me! Would love to learn.

Cheers.

Regards,
Barry