## MHD: HARTMANN PROBLEM 2D

Numerical methods and mathematical models of Elmer
Andrea_P
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### MHD: HARTMANN PROBLEM 2D

Hi,
I have replicated the 2D problem present at this link: http://woodruffscientific.com/files/hcll2Report.pdf (physical and geometry info page 19). Unfortunately, I am not able to obtain the same curves reported in the attached image. For Ha>100 the system diverges. Besides for Ha= 100 the velocity profile appears faster at the domain contours and it does not take over the classic parabolic shape. Has anyone got any idea about solving this problem?
Regards,
Andrea
Attachments
REPORT PANCHALL.zip
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POLYTECHNIC UNIVERSITY OF TURIN-DIMEAS
kevinarden
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### Re: MHD: HARTMANN PROBLEM 2D

Elmer is not as focused on turbulent flow as openfoam is. It doesn't take much to get some turbulence in flow problems. In general it will take finer meshes, smaller time steps, and higher order elements than if using openfoam turbulent solvers.

There are also turbulent flow solvers in Elmer that could be included such as k-epsilon that would be of benefit.

viewtopic.php?f=3&t=6995&hilit=turbulent
Andrea_P
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### Re: MHD: HARTMANN PROBLEM 2D

Hi Kevin,
the pdf says that the flow is laminar, so could it be turbulent in Elmer?
-Andrae
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kevinarden
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### Re: MHD: HARTMANN PROBLEM 2D

No if it is laminar it is laminar. The viscosity in the sif is not the same as in the report. I did not have any convergence issues when I used the viscosity in the report.
kevinarden
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### Re: MHD: HARTMANN PROBLEM 2D

The issue is at the boundary, the report says you have to have a very fine mesh at the boundary. It also mentions boundary layer approach. I went with a fine higher order quad mesh and started getting better results at the boundary away from the inlet.
result.png
(139.88 KiB) Not downloaded yet
beam.grd
(630 Bytes) Downloaded 25 times
ycase.sif
(2.82 KiB) Downloaded 24 times
Andrea_P
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### Re: MHD: HARTMANN PROBLEM 2D

kevinarden wrote: 18 May 2021, 12:23 No if it is laminar it is laminar. The viscosity in the sif is not the same as in the report. I did not have any convergence issues when I used the viscosity in the report.
Hi Kevin,
Thanks for your rapid answer. The viscosity in the ycase.sif is the same present in my original case.sif, so is the value different from that one in the report? Could I edit your case.sif in this way?:

Code: Select all

Header
CHECK KEYWORDS Warn
Mesh DB "." ""
Include Path ""
Results Directory ""
End
or would it be better to keep

Code: Select all

Mesh DB "." "beam"
and use Elmer grid? I have tried with Ha= 500 but the solution diverges.
-Andrea
Attachments
case.sif
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POLYTECHNIC UNIVERSITY OF TURIN-DIMEAS
kevinarden
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### Re: MHD: HARTMANN PROBLEM 2D

The mesh in beam is very fine, and uses higher order elements. The solution in the middle is likely not affected but results at the boundary would be.
Andrea_P
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### Re: MHD: HARTMANN PROBLEM 2D

kevinarden wrote: 18 May 2021, 18:04 The mesh in beam is very fine, and uses higher order elements. The solution in the middle is likely not affected but results at the boundary would be.
Hi Kevin,
I have just run the case after have used

Code: Select all

ElmerGrid 1 2 beam.grd
, but it keeps diverging for Ha=500 and viscosity = 3.925e-4. Sorry, I did not understand your last answer.
-Andrea
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kevinarden
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### Re: MHD: HARTMANN PROBLEM 2D

When I change Ha to 500 it does diverge, so I either have to use a finer mesh, a smaller time step, or both. Or add a boundary layer solver.
Andrea_P
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### Re: MHD: HARTMANN PROBLEM 2D

kevinarden wrote: 18 May 2021, 20:05 When I change Ha to 500 it does diverge, so I either have to use a finer mesh, a smaller time step, or both. Or add a boundary layer solver.
Does this kind of solver exist in Elmer?
-Andrea
POLYTECHNIC UNIVERSITY OF TURIN-DIMEAS