Mesh size vs Convergence

Xuekun · January 16, 2016, 07:56

Hello all,

I am modelling the gas flow through the channel. I have a problem about the modelling size scale vs the convergence.

Previously I imported the mesh, using the default units:m, the model converged very well under the specified boundary condition, which is pressure outlet at both sides, with the inlet side higher pressure.

Actually, if I scaled the mesh down by 1E-6, which change the length scale from m to um, the model never converged, no matter using the same boundary condition or changing to whatever. I checked that, after I scaled the mesh, the minimum cell volume is 1E-22 m3, is this the problem causing the divergence? Please help !

Thanks !

JSped · January 17, 2016, 16:57

I am new to CFD but that seems incredibly small. How many total cells is that?

When you say it hasn't converged, do you mean in the same number of iterations as before?

Xuekun · January 17, 2016, 19:24

Quote:

Originally Posted by JSped

I am new to CFD but that seems incredibly small. How many total cells is that?

When you say it hasn't converged, do you mean in the same number of iterations as before?

Hi,

Thanks to your response ! The cell count is 2 million. By saying not converge, I mean the residuals always increase after 10 iterations. I solved this problem by deleting some smallest cells. Thanks again for your reply !

fluid23 · January 18, 2016, 15:27

First... What kind of geometry did you model that you could scale the geometry by a factor of 1/1,000,000? That seems very excessive and unnecessary to me. Is this just an exercise or are you trying to get some real quantifiable scientific or engineering value from this analysis? To put this in to terms that someone could understand, this would be the equivalent of scaling mount Everest from its height of 29,029 feet to something about the size of your finger nail.

Second, you most likely are running into your machine epsilon (i.e. the rounding error of floating point numbers). This varies depending on your machine architecture, but having cell sizes on the order of 10^-22 would definitely put you in the 'danger zone' Basically, anything smaller than machine epsilon (which for double precision is somewhere around 10^-11) will get stored as zero, not the value you intended. This is probably why you got better results deleting the smallest cells.

Xuekun · January 24, 2016, 07:54

Quote:

Originally Posted by MBdonCFD

First... What kind of geometry did you model that you could scale the geometry by a factor of 1/1,000,000? That seems very excessive and unnecessary to me. Is this just an exercise or are you trying to get some real quantifiable scientific or engineering value from this analysis? To put this in to terms that someone could understand, this would be the equivalent of scaling mount Everest from its height of 29,029 feet to something about the size of your finger nail.

Second, you most likely are running into your machine epsilon (i.e. the rounding error of floating point numbers). This varies depending on your machine architecture, but having cell sizes on the order of 10^-22 would definitely put you in the 'danger zone' Basically, anything smaller than machine epsilon (which for double precision is somewhere around 10^-11) will get stored as zero, not the value you intended. This is probably why you got better results deleting the smallest cells.

Hello Matt,

Thank you so much for your reply ! It seems make sense if explained as machine epsilon problem. I actually intended to model the gas diffusion phenomenon in the porous sample, and I have the real structure 3D mesh. The real size is 10 * 10* 10 microns. If I keep consistent with what I model and what is real in terms of feature size, then the cell volume will definitely go to 1E-22 um3 level, at a moderate mesh size. So how can I deal with this problem?

fluid23 · January 25, 2016, 09:10

To be honest, I am really not sure how to approach that. I have never worked so small before. You can find a similarity solution, at least to some degree, by changing your fluid properties such that your reynolds number stays constant but the characteristic length can grow. I am not sure this is the correct approach for this problem, perhaps someone else can weigh in who has more experience.

January 16, 2016, 07:56	Mesh size vs Convergence	#1
Xuekun New Member Xuekun Lu Join Date: Oct 2015 Posts: 20 Rep Power: 10	Hello all, I am modelling the gas flow through the channel. I have a problem about the modelling size scale vs the convergence. Previously I imported the mesh, using the default units:m, the model converged very well under the specified boundary condition, which is pressure outlet at both sides, with the inlet side higher pressure. Actually, if I scaled the mesh down by 1E-6, which change the length scale from m to um, the model never converged, no matter using the same boundary condition or changing to whatever. I checked that, after I scaled the mesh, the minimum cell volume is 1E-22 m3, is this the problem causing the divergence? Please help ! Thanks !

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January 17, 2016, 16:57		#2
JSped New Member James Join Date: Jan 2016 Posts: 3 Rep Power: 10	I am new to CFD but that seems incredibly small. How many total cells is that? When you say it hasn't converged, do you mean in the same number of iterations as before?

January 18, 2016, 15:27		#4
fluid23 Senior Member Matt Join Date: Aug 2014 Posts: 947 Rep Power: 18	First... What kind of geometry did you model that you could scale the geometry by a factor of 1/1,000,000? That seems very excessive and unnecessary to me. Is this just an exercise or are you trying to get some real quantifiable scientific or engineering value from this analysis? To put this in to terms that someone could understand, this would be the equivalent of scaling mount Everest from its height of 29,029 feet to something about the size of your finger nail. Second, you most likely are running into your machine epsilon (i.e. the rounding error of floating point numbers). This varies depending on your machine architecture, but having cell sizes on the order of 10^-22 would definitely put you in the 'danger zone' Basically, anything smaller than machine epsilon (which for double precision is somewhere around 10^-11) will get stored as zero, not the value you intended. This is probably why you got better results deleting the smallest cells.

January 25, 2016, 09:10		#6
fluid23 Senior Member Matt Join Date: Aug 2014 Posts: 947 Rep Power: 18	To be honest, I am really not sure how to approach that. I have never worked so small before. You can find a similarity solution, at least to some degree, by changing your fluid properties such that your reynolds number stays constant but the characteristic length can grow. I am not sure this is the correct approach for this problem, perhaps someone else can weigh in who has more experience.