# Varying Results from Different Mesh Sizes

I'm trying to solve a simple 2D problem (fluid passing round pillars, *see attached figure 1*) in micro scale (drew in mm, scaling in "Setup") with the boundary conditions of pressure inlet & outlet, symmetry up & down, and no-slip wall for pillars (arcs in the figure 1).

The problem is when I change the mesh size, the result came out very different (factor of 2 to even 10) under the same convergence criteria. And when I change the convergence criteria (from __1e-3 to 1e-5__, several trials in between) with the same mesh size, the results still vary a lot. The velocity profiles physically make sense (*see attached figure 2*), but the values just do not match.

I don't see this to be a simple problem of mesh size (*i.e.* not enough cells) or convergence criteria (*i.e. *not converged yet), because we had the exactly same case for 3D, which has finer mesh and much more cells, and that never gave us a problem like this. For example, under the convergence criteria of 1e-3, the results from different mesh sizes are within 1% error. And the error is also within 1% when the convergence criteria is 1e-4. The results match pretty well under all conditions.

Any kinds of help will be appreciated!

Figure 1 - Geometry & Mesh

Figure 2 - Results - Velocity Profile

## Comments

as ansys employee we can not download attachments. please insert some images of mesh and set up.

did you carry mesh independent study for this case. you may want to use it.

Also review what you're seeing change. If it's a facet maximum is it a meaningful number?

Hello,

Thank you for your patience.

What Keyur is talking about is this - Your CFD solution needs to be mesh independent. When you lower the mesh size, the CFD solution will be different. Beyond a certain amount of grid refinement, you will start seeing smaller variation in results. You need to be at that level of grid refinement to ensure that your CFD solution no longer depends on the grid sizes, in other words - grid independent.

About your solution varying with convergence criteria, when you max velocity varies with convergence criteria, it means you have not achieved convergence. It is possible that your velocities are oscillating with iteration. If you have not done so already, please ensure you're monitoring the average outlet velocity, inlet pressure etc. as a function of iterations. This will help you understand if you've achieved steady state results. Also, use the lower convergence criteria to make sure the solution is fully converged. Please share a plot of your convergence, if that is possible to we can understand things better.

Also, in your above table, what are the units of the mesh size you have selected?

What is the diameter of your micro-pillars? Have you checked if your minimum grid size is still with in the continuum assumption? You might want to calculate the Knudsen number to double check. Please refer to the following article for additional details on this. If your Knudsen number is close to or greater than 1, you are no longer operating under the continuum assumption and results from Navier Stokes hold no meaning.

https://en.wikipedia.org/wiki/Knudsen_number

I hope this helps and look forward to your reply.

Best Regards,

Karthik

Hi Karthik,

Thank you so much for your reply. Just to make sure, do you mean my mesh size is still too large for convergence? But in the 3D case (the above 2D case + a dimension in height), these mesh sizes (5E-5 to 7.5E-5) work fine and give me good convergence. I have compared the 3D results against some literatures, and it showed good agreement, so I thought the mesh size is small enough but I could be wrong.

As for your questions, the mesh sizes are in meters, and the diameter of the pillars are 2.5 mm (I drew the geometry and did the meshing in mm scale, and scaled it to micron scale when solving the problem in "setup").

I don't quite understand what do you mean by "within continuum assumption". This is a problem of water passing pillars, so the continuity equation will always hold during solving the problem. Also, is Knudsen number valid for liquids? I'll appreciate it if you can explain a little more.

Thanks again for the help!

Best,

Ruisong

Hi Karthik,

I forgot to mention that when we are solving the 2D and 3D cases (same geometry and same mesh size), the case converges faster with a correct result (as I mentioned above), while in the 2D case, the continuity residual drops very slowly, so it takes very long time to converge and the results are varying a lot as the problem description.

We were expecting that the 2D case converges much faster than 3D, but it does not (2D is faster for each iteration of course, but the total iterations is much larger than 3D). Also, the continuity residual fluctuates a lot after a few thousands iterations (suddenly rises and fluctuates, and then dropping down and repeating the fluctuation). Does this mean there is a problem with the continuum assumption? Thanks.

Ruisong

Hello Ruisong,

Can you check the domain extents of your mesh and post the screenshot? You should be able to check this under 'Scale' in Fluent.

Knudsen number is valid for any fluid - liquid or gas. At large Knudsen numbers, the fluid becomes rarified where the molecular spacing of the fluid is compared to the length scale of the problem and bulk fluid properties such as density and viscosity do not have any meaning at that scale. And hence one cannot solve NS equations at that scale. I do not believe that is the case with your simulation. However, it would be prudent to verify.

Please have to look at your grid independence. It is quite possible that your solutions are not truly grid independent. Also, when you are performing these grid independent studies, it is important to ensure deep convergence. Make sure you have a sufficiently low convergence criterion for all your equations.

Please share your findings here. I hope this helps.

Best,

Karthik

Hi Karthik,

Thanks for the reply. I have inserted the domain extents below. The Knudsen number is much smaller than 1 (at the magnitude of 1 E-5 to 1 E-4), so it's not a continuum issue.

Do you have any idea why 3D case works well but 2D fails (as mentioned in my previous reply)? I was using the same convergence criteria and mesh sizes, which is why I don't think this is a problem of grid independence (i.e. the mesh size is small enough for 3D case, so it should be small enough for 2D).

Also, it was taking very long (maybe 2 hours to achieve convergence criteria of 1E-4, which is not small enough) to solve the 2D problem, and this is not what we expected for such a simple 2D geometry.

Thank you.

Best,

Ruisong

Hi Karthik,

As I have mentioned before, I feel it weird that the 2D case does not work. So I tested a simple 2D problem (inserted below, pressure inlet & outlet + No-slip + symmetry) and it took 50,000 iterations (almost 1 hour) to converge (at the criteria of 1E-6). This makes no sense to me, since this is the easiest problem I can think of to run a CFD.

For the geometry below, it 10 micron * 5 micron (drew in mm, scaled to microns in "setup", mesh size at 7.5 E-5 m).

Given the situation that we do not have problems with 3D case, is there anything specific we need to pay attention to in solving a 2D problem?

Thanks.

Best,

Ruisong

Whilst you're OK for the Knudsen Number (please check the definition as it's a dimensionless number that is sometimes defined as the inverse of it's self!) at 5 microns you're also going to have all sorts of interesting effects. I'd missed the images being added as I've run small scale models at various times at University & in ANSYS.

Please can you add vertical lines and plot the velocity against the y position? Not sure why 3d would be more stable unless that's just giving the numerics extra space (equations) to hide problems.

When you come to do this in experiments you may find all sorts of things happening in the flow: the surface finish may even give meaningful differences in channel size and electro-static interactions can become incredibly important.

Are you running double precision?

Hello,

Thanks for the reply! I have inserted pictures of velocity against the y position (vector plot). I'm not sure if this is clear enough.

I've also plotted a y velocity distribution, which is not symmetric even if the solution is converged in this simple 2D case. This is confusing.

I'm running double precision. Thank you.

Velocity v should be the y component of the velocity, and I'd expect that to be about zero. What do the u-velocity & magnitude look like? Please also add the residual plot: you'll need to converge beyond the default criterion at this scale.

Hi,

I have inserted the velocity magnitude (1st pic), u velocity (2nd pic) and the residual (3rd pic). Thanks.

Weird, can you plot the velocity contour in Fluent. Also, did you take all of the data from Fluent or CFD Post?

Hi,

I have inserted the velocity contour below. The residual plot and the contour are from FLUENT, and the velocities (magnitude & x & y) are from CFD post.

Thank you.

Dear All,

I have been trying to compute the internal leakage for a 3-D servo valve geometry. However, I encountered some challenges particularly for meshing the micron size geometry with utilizing the Ansys meshing tools. In addition, I need more help for the numerical modeling of this complex geometry in Ansys Fluent. I mean, I am wondering that how to set up the physics and select the models for the rest of the numerical model.

The main drawback stemming from this meshing process is that the sharp edges can be rounded with a small radius; despite being very small, this micro radius can change the spool valve null region characteristics, which have an important influence on the valve performance. Therefore, if you are able to provide us some tutorials or videos, which explain how to mesh for the micro radius that will be more appreciated. In addition, I am including a reference paper that illustrates a 2D computational fluid dynamics (CFD) numerical results that are generic, and they can be applicable to any servo valve. Furthermore, the literature has 2D numerical studies for calculating the internal leakage but, I need a detailed 3D numerical model to delve into the geometry imperfection effects on the internal leakage of the servo valve.

If you have any further questions, please do not hesitate to contact with me. Any kind help will be more appreciated.

Thank you.

Best regards,

I have been trying to compute the internal leakage for a 3-D servo valve geometry. However, I encountered some challenges particularly for meshing the micron size geometry with utilizing the Ansys meshing tools. In addition, I need more help for the numerical modeling of this complex geometry in Ansys Fluent. I mean, I am wondering that how to set up the physics and select the models for the rest of the numerical model.

The main drawback stemming from this meshing process is that the sharp edges can be rounded with a small radius; despite being very small, this micro radius can change the spool valve null region characteristics, which have an important influence on the valve performance. Therefore, if you are able to provide us some tutorials or videos, which explain how to mesh for the micro radius that will be more appreciated. In addition, I am including a reference paper that illustrates a 2D computational fluid dynamics (CFD) numerical results that are generic, and they can be applicable to any servo valve. Furthermore, the literature has 2D numerical studies for calculating the internal leakage but, I need a detailed 3D numerical model to delve into the geometry imperfection effects on the internal leakage of the servo valve.

If you have any further questions, please do not hesitate to contact with me. Any kind work will be more appreciated.

Thank you.

Best regards,

@mech2 Create a New Discussion. It's not a good idea to add a new topic as a comment at the end of a very long discussion.

One suggestion for meshing very small features is to scale up the geometry in CAD before taking it in to mesh in ANSYS meshing. Then in Fluent, scale the mesh back down to the true size.