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Minimum mesh size for Advection-Diffusion Problem

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Old   March 3, 2015, 07:35
Default Minimum mesh size for Advection-Diffusion Problem
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Eoin Murphy
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Hi all,

I'm currently working on an advection-diffusion problem (in Ansys CFX) and during my mesh convergence study when I refine my mesh down below a certain level the solver doesn't converge. I have several different models and the problem arises with a model which has non-linear diffusivity.

In addition, I should say that the simulation is steady-state and the flow is entirely laminar, solved using double precision, and in test cases, has no significant flow features, i.e., simple flow along a flat surface with a fully developed flow at inlet. The diffusivity of the transported additional variable itself is non-linear and is in the region of 1E-12m^2/s in places and is dependent on several parameters and variables, including the shear-strain rate.

Below is a screen capture of the boundary layer with the mesh shown that does solve fine. Any significant refinement of this model results in the solution becoming unstable. At present for this mesh to solve I need to run it at a physical timescale several orders of magnitude less than the auto-derived one, and using initial values derived by a simpler model.

Boundary Layer.jpg

Firstly, is there a minimum mesh size which I should not go below,
and secondly, is there a way to calculate this?

I have seen posts before about minimum mesh size but nothing specific to this.

http://www.cfd-online.com/Forums/cfx...fine-mesh.html

Thanks for your time and help,

Eoin

Last edited by Murf; March 3, 2015 at 12:15. Reason: not enough details given in previous version.
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Old   March 3, 2015, 18:33
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Glenn Horrocks
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Numerical instability increases as mesh size decreases. So convergence problems with mesh refinement can occur on tricky simulations. This occurs as finer meshes have less numerical dissipation so instabilities are less damped.

There is no simple way of calculating when you will have problems. Have a look at the textbooks on CFD stability for more information - I think "Computational Fluid Dynamics" by Roache has a discussion about this. It has been a while since I read this book so I am not sure it does, but it is an excellent reference on many issues regarding accuracy and stability of CFD simulations.
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Old   March 4, 2015, 07:46
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Eoin Murphy
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Cheers Glenn.

I'll take a look at that.
Thanks,

Eoin
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Old   March 4, 2015, 18:49
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The normal things to look at when you have round off errors are:
* Double precision (you are already doing that I think)
* Improve mesh quality, so decrease aspect ratios and make the mesh more orthogonal.
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Old   March 5, 2015, 15:15
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Hi Glenn,

Yes, double precision for all simulations.
I've been working a lot on producing a mesh with better quality in ICEM for my more complicated geometries, so it's good to know I'm on the right track. I'll keep going with that.

Thanks again,

Eoin
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