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Mesh convergence analysis
Posted Sep 29, 2010, 12:24 p.m. EDT 4 Replies
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Hello everyone,
Q: What is the purpose of mesh convergence analysis, practically?
I am doing mesh analysis by subdividing the max mesh size on the outer cylinder boundary (in cylinder in the flow example), and hence measure as accurate scalar A as possible (e.g. drag). The most ideal case of mesh has a drag of say 30, which I tried by using a very very high mesh. But my easier subdivision case studies always come close to 30, say 34, 32, 48,128 (which apparently 128 is too far).
So does this mean that I can use the value of the mesh that corresponds to 34 and 32 safely for trying different (and/or lower hence easier) flow velocities? i.e. to say that meshes of 32 and 34 are good enough for my simulation? or should I find the one that corresponds as close as possible to 30 (which is quite impractical).
Please help to clear my confusion,
Q: What is the purpose of mesh convergence analysis, practically?
I am doing mesh analysis by subdividing the max mesh size on the outer cylinder boundary (in cylinder in the flow example), and hence measure as accurate scalar A as possible (e.g. drag). The most ideal case of mesh has a drag of say 30, which I tried by using a very very high mesh. But my easier subdivision case studies always come close to 30, say 34, 32, 48,128 (which apparently 128 is too far).
So does this mean that I can use the value of the mesh that corresponds to 34 and 32 safely for trying different (and/or lower hence easier) flow velocities? i.e. to say that meshes of 32 and 34 are good enough for my simulation? or should I find the one that corresponds as close as possible to 30 (which is quite impractical).
Please help to clear my confusion,
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4 Replies Last Post Oct 7, 2010, 4:40 a.m. EDT
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Posted:
1 decade ago
I would say, the main question is: how exact should the result be or more general: what do you do want to do with the results?
Then, another question is: how can the error of scalar A be extrapolated to other cases/parameters or other scalars.
At least, i think the "extrapolation of errors" strongly depends on the model. But normally, if you reduce Re-Number, the results should not be more incorrect than at higher Re-numbers?!?
I don't know, maybe you already know about this paper, but I think this deals partly with that problem.
P. J. Roache: "QUANTIFICATION OF UNCERTAINTY IN COMPUTATIONAL FLUID DYNAMICS"
www.nd.edu/~cpenning/ame30362s06/Roache_fluid_dynamics_review.pdf
hope this helps
Then, another question is: how can the error of scalar A be extrapolated to other cases/parameters or other scalars.
At least, i think the "extrapolation of errors" strongly depends on the model. But normally, if you reduce Re-Number, the results should not be more incorrect than at higher Re-numbers?!?
I don't know, maybe you already know about this paper, but I think this deals partly with that problem.
P. J. Roache: "QUANTIFICATION OF UNCERTAINTY IN COMPUTATIONAL FLUID DYNAMICS"
www.nd.edu/~cpenning/ame30362s06/Roache_fluid_dynamics_review.pdf
hope this helps
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Posted:
1 decade ago
Hi
with the smoothed view it's always difficult to juge if the mesh denisty is more or less OK. I usually check that with a wireframe and "no-refinements" selected.
Personally I'm mostly happy when I have < 5% change for a mesh doubling (provided that the mesh density is really doubling in the critical regions), but I have noticed that COMSOL allows me to get easily <1% without exploding my RAM. Then I also check which parameters changes, the dependent variables as well as the derived ones I interested in. But CFD is probably somewhat more critcal than structural ;)
--
Good luck
Ivar
with the smoothed view it's always difficult to juge if the mesh denisty is more or less OK. I usually check that with a wireframe and "no-refinements" selected.
Personally I'm mostly happy when I have < 5% change for a mesh doubling (provided that the mesh density is really doubling in the critical regions), but I have noticed that COMSOL allows me to get easily <1% without exploding my RAM. Then I also check which parameters changes, the dependent variables as well as the derived ones I interested in. But CFD is probably somewhat more critcal than structural ;)
--
Good luck
Ivar
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Posted:
1 decade ago
I see your points. Many thanks for the insightful comments K. and Ivar.
A number like Nusselt number is a combination of several parameters.
Let's say (incorrect but simply) that
Nu_local = Flux / (T-T_bulk) ---------------- at each node
and
Nu_average = Int (Nu_local)/Int (1) ------------- defined on the cylinder boundary
Then both flux calculation and T values at the boundary becomes important.
Then when I do a mesh study on the cylinder perimeter I get figure 1. As you notice as the mesh size (x axis) decreases I get a better Nusselt number, but then it starts going down like crazy. That mesh size is already too small, which makes the model impractical. So, the question is this: Is the mesh good enough at the middle range?
There maybe many factors that affect this behavior:
1) Artificial diffusion. I heard from support as the mesh size reduces, the error introduced should get lower. But who knows how it works under the hoods.
2) Comsol's calculation of boundary values between two adjacent domains. As the mesh gets smaller T1 (of domain cylinder) gets closer to T2 (of domain fluid).
3) Calculation of Integrals. Since reacf is a summation integral and I still have T which is not. does Int(reacf(T)/(T-Tbulk)) work as expected? It was much more stable with Comsol's total flux functions. Less accurate but stable.
Already too long to read, so I stop here.
I'm all ears.
A number like Nusselt number is a combination of several parameters.
Let's say (incorrect but simply) that
Nu_local = Flux / (T-T_bulk) ---------------- at each node
and
Nu_average = Int (Nu_local)/Int (1) ------------- defined on the cylinder boundary
Then both flux calculation and T values at the boundary becomes important.
Then when I do a mesh study on the cylinder perimeter I get figure 1. As you notice as the mesh size (x axis) decreases I get a better Nusselt number, but then it starts going down like crazy. That mesh size is already too small, which makes the model impractical. So, the question is this: Is the mesh good enough at the middle range?
There maybe many factors that affect this behavior:
1) Artificial diffusion. I heard from support as the mesh size reduces, the error introduced should get lower. But who knows how it works under the hoods.
2) Comsol's calculation of boundary values between two adjacent domains. As the mesh gets smaller T1 (of domain cylinder) gets closer to T2 (of domain fluid).
3) Calculation of Integrals. Since reacf is a summation integral and I still have T which is not. does Int(reacf(T)/(T-Tbulk)) work as expected? It was much more stable with Comsol's total flux functions. Less accurate but stable.
Already too long to read, so I stop here.
I'm all ears.
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Posted:
1 decade ago
I was talking to a PostDoc yesterday and he told me that if there is such a "S" shape behavior of your mesh study curve there should be something wrong with the model. I am not sure what to say so far, as I am not sure about when Artificial Diffusion kicks in, or other underlying comsol, since my model is simple enough.
Any ideas?
--
Comsol 4.0a
Ubuntu 10.04.1
Any ideas?
--
Comsol 4.0a
Ubuntu 10.04.1