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Adaptive moving mesh for time dependant problems - need some help with stability.

Posted Feb 19, 2010, 4:48 a.m. EST Mesh 11 Replies

Michael Welland
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Hi everyone, I've been trying to implement an adaptive moving mesh for a time dependent problem. Basically, the idea is that you try to move mesh elements to regions where you need a finer mesh (for example, a large gradient in a dependent variable). The total number of elements doesn't actually change (on the reference domain), but their spatial mapping does. this is nice because as the problem progresses, the mapping can change to move with your large gradient. Result: potentially large reduction in required mesh elements!

The problem is incredibly non-linear, as you might imagine and inverted mesh elements run rampant. Currently, I can get it to converge nicely by tweaking the nonlinear solver settings but this runs very slowly. Alternately, I can make it run quickly, but with substantial inverted elements and NL fails.

I've run out of ideas of how to obtain this dream in a stable and efficient manner. Does anybody have some advice? I attach my sim file for reference (the mathematical derivation is widely available in literature).

Thanks,
Mike

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11 Replies Last Post Jan 13, 2012, 4:54 a.m. EST
Danial Tz
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Posted: 1 decade ago Feb 19, 2010, 6:38 a.m. EST
I know that these guys did it in my university. In case you've not seen it:
www-m2.ma.tum.de/foswiki/pub/M2/Allgemeines/ProfessorSimeon/plinningersimeon.pdf

maybe it can give you some ideas. At the end, your solution will make our life lot easier.
I know that these guys did it in my university. In case you've not seen it: http://www-m2.ma.tum.de/foswiki/pub/M2/Allgemeines/ProfessorSimeon/plinningersimeon.pdf maybe it can give you some ideas. At the end, your solution will make our life lot easier.
Michael Welland
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Posted: 1 decade ago Feb 22, 2010, 7:59 a.m. EST
Thanks Daniel, this is a very interesting paper which I hadn't seen before.

Best,
Mike
Thanks Daniel, this is a very interesting paper which I hadn't seen before. Best, Mike
Clinton Canaday
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Posted: 1 decade ago Sep 24, 2010, 12:44 p.m. EDT
I would very much like to see this implemented somehow. I have a 3D model in which a transient heat source is moving through elasto-plastic material and would like to save DOF where it's not needed. Ultimately, I need to save computation time and automatically refine where needed. I'll take a stab at it based on the paper posted, but if someone else has been successful, any help would be most appreciated.
I would very much like to see this implemented somehow. I have a 3D model in which a transient heat source is moving through elasto-plastic material and would like to save DOF where it's not needed. Ultimately, I need to save computation time and automatically refine where needed. I'll take a stab at it based on the paper posted, but if someone else has been successful, any help would be most appreciated.
Michael Welland
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Posted: 1 decade ago Sep 28, 2010, 10:04 a.m. EDT
Hi Clinton,

I am happy that this thread is not yet dead! I suspended my own investigation on this due to lack of convergence but would be very interested if you have success!

I briefly flirted with the idea of recasting the 2-D time dependent problem into a 3-D stationary problem (time as the axis) and then letting the adaptive meshing stationary solver chew through it with the idea being that it could locally refine both space and time resolution. The result was massive RAM consumption and paging which eventually ground progress to a halt. Maybe it would be useful for you though?

Cheers,
Mike
Hi Clinton, I am happy that this thread is not yet dead! I suspended my own investigation on this due to lack of convergence but would be very interested if you have success! I briefly flirted with the idea of recasting the 2-D time dependent problem into a 3-D stationary problem (time as the axis) and then letting the adaptive meshing stationary solver chew through it with the idea being that it could locally refine both space and time resolution. The result was massive RAM consumption and paging which eventually ground progress to a halt. Maybe it would be useful for you though? Cheers, Mike
Quang Tuyen Tran
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Posted: 1 decade ago Jan 11, 2012, 7:32 a.m. EST

Hi,

i have a problem with Moving mesh in a simulation with phase change. i want to use moving mesh method to solve two-dimensional Phase change problems with natural convection.The difficulty in solving these problem is the presence of the moving interface between the solid and liquid regions.

Have you ideas?

Thank you very much
--
------------------------------
Best regards
QTran
Hi, i have a problem with Moving mesh in a simulation with phase change. i want to use moving mesh method to solve two-dimensional Phase change problems with natural convection.The difficulty in solving these problem is the presence of the moving interface between the solid and liquid regions. Have you ideas? Thank you very much -- ------------------------------ Best regards QTran
Michael Welland
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Posted: 1 decade ago Jan 11, 2012, 8:03 a.m. EST
Hi QTran, I'm not exactly sure what your problem is specifically. I don't have much experience with natural convection but I understand it to be quite unstable, so I wish you luck integrating it with a moving boundary!

Pretty much all of my experience with the Stefan approach to phase change is in my thesis (www.mikewelland.com/publications/phdthesis) so you can take a look at that. Does the topology of your problem change (ie: do your interfaces join, split or dissappear / appear?) If so you could take a look at using the phase-field model too (also in the thesis although an early formulation).

Good luck!
Mike
Hi QTran, I'm not exactly sure what your problem is specifically. I don't have much experience with natural convection but I understand it to be quite unstable, so I wish you luck integrating it with a moving boundary! Pretty much all of my experience with the Stefan approach to phase change is in my thesis (http://www.mikewelland.com/publications/phdthesis) so you can take a look at that. Does the topology of your problem change (ie: do your interfaces join, split or dissappear / appear?) If so you could take a look at using the phase-field model too (also in the thesis although an early formulation). Good luck! Mike
Quang Tuyen Tran
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Posted: 1 decade ago Jan 11, 2012, 9:10 a.m. EST

Hi Mike,

thank you for your answer, i would like to make a simulation of phase change by freezing, the fluid is water, in the attach file you can see my modell. You know that when a material changes phase, for instance from liquid to solid, energy is added to the liquid, the mesh at first is fine near the solid (zylinder) but after the phase change, there is solid (ice), and ofcourse the mesh must change at the interface between Solid and liquid.


--
------------------------------
Best regards
QTran
Hi Mike, thank you for your answer, i would like to make a simulation of phase change by freezing, the fluid is water, in the attach file you can see my modell. You know that when a material changes phase, for instance from liquid to solid, energy is added to the liquid, the mesh at first is fine near the solid (zylinder) but after the phase change, there is solid (ice), and ofcourse the mesh must change at the interface between Solid and liquid. -- ------------------------------ Best regards QTran

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Michael Welland
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Posted: 1 decade ago Jan 11, 2012, 9:29 a.m. EST
Hi again,
As I understand it, you are looking to implement the Stefan model for phase change with a moving mesh. It is a fairly common technique for the sort of thing and there are several resources available. In the thesis, the derivation is on page 33 (ignore the mass transport part).

Good luck!

Hi again, As I understand it, you are looking to implement the Stefan model for phase change with a moving mesh. It is a fairly common technique for the sort of thing and there are several resources available. In the thesis, the derivation is on page 33 (ignore the mass transport part). Good luck!
Michael Welland
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Posted: 1 decade ago Jan 11, 2012, 9:33 a.m. EST
Hi again,
As I understand it, you are looking to implement the Stefan model for phase change with a moving mesh. It is a fairly common technique for the sort of thing and there are several resources available. In the thesis, the derivation is on page 33 (ignore the mass transport part).

Good luck!

Hi again, As I understand it, you are looking to implement the Stefan model for phase change with a moving mesh. It is a fairly common technique for the sort of thing and there are several resources available. In the thesis, the derivation is on page 33 (ignore the mass transport part). Good luck!
Quang Tuyen Tran
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Posted: 1 decade ago Jan 13, 2012, 4:35 a.m. EST

Hi Mike,

i understand these theories, but i don't know how to used it with Comsol, can you give me a example.

Thank you very much
--
------------------------------
Best regards
QTran
Hi Mike, i understand these theories, but i don't know how to used it with Comsol, can you give me a example. Thank you very much -- ------------------------------ Best regards QTran
Michael Welland
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Posted: 1 decade ago Jan 13, 2012, 4:54 a.m. EST
The Comsol report with my implementation of the Stefan model is in the Appendix of the thesis. My project required new phases starting and ending, which required a more complicated implementation via MatLab, but I think what you are looking for should be in there.

Attached is a demo I made a while ago. It should be sufficient to get you started.
The Comsol report with my implementation of the Stefan model is in the Appendix of the thesis. My project required new phases starting and ending, which required a more complicated implementation via MatLab, but I think what you are looking for should be in there. Attached is a demo I made a while ago. It should be sufficient to get you started.

Attachments:

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