MHD: HARTMANN PROBLEM 2D

Numerical methods and mathematical models of Elmer
kevinarden
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Re: MHD: HARTMANN PROBLEM 2D

Post by kevinarden »

I refined the mesh, and reduced the time step, to obtain the convergence, and yes there is a boundary layer method in Elmer.
resut500.png
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ycase.sif
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beam.grd
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kevinarden
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Re: MHD: HARTMANN PROBLEM 2D

Post by kevinarden »

This is an example of a boundary layer solution

https://github.com/ElmerCSC/elmerfem/tr ... ts/Step_ke
Andrea_P
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Re: MHD: HARTMANN PROBLEM 2D

Post by Andrea_P »

kevinarden wrote: 18 May 2021, 21:07 I refined the mesh, and reduced the time step, to obtain the convergence, and yes there is a boundary layer method in Elmer.

resut500.png
ycase.sif
beam.grd
Hi Kevin,
I do not know how I can express my gratitude. I am going to prove it right now. I will let you know.
Regards,
Andrea
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Andrea_P
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Re: MHD: HARTMANN PROBLEM 2D

Post by Andrea_P »

kevinarden wrote: 18 May 2021, 21:07 I refined the mesh, and reduced the time step, to obtain the convergence, and yes there is a boundary layer method in Elmer.

resut500.png
ycase.sif
beam.grd
Hi Kevin,
I have plotted the analytical solution by the equation present in the same report and there is a big difference with respect to the results in Elmer. How is it possible?
-Andrea
Attachments
analitical_solution.png
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kevinarden
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Re: MHD: HARTMANN PROBLEM 2D

Post by kevinarden »

My results appear to match the report, I would have to see the files used.
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Re: MHD: HARTMANN PROBLEM 2D

Post by Andrea_P »

kevinarden wrote: 19 May 2021, 11:48 My results appear to match the report, I would have to see the files used.
Hi Kevin,
Indeed the results match those of the report, however if you look at page 19, there is the analytic equation. If you solve it, for instance in Matlab or python, you will realize the deep difference.
-Andrea
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formula.jpg
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Andrea_P
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Re: MHD: HARTMANN PROBLEM 2D

Post by Andrea_P »

kevinarden wrote: 19 May 2021, 11:48 My results appear to match the report, I would have to see the files used.
Hi Kevin,
I share the analytic results achieved by the Hartmann velocity profile equation encountered here https://www.researchgate.net/publicatio ... m_extended (page 16). I have used it and I have obtained the Elmer results.
-Andrea
Attachments
analitical_solution.png
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formula.jpg
formula.jpg (25.43 KiB) Viewed 47362 times
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raback
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Re: MHD: HARTMANN PROBLEM 2D

Post by raback »

Hi

The curves look awfully similar to me. Seems like a scaling issue. I think the 1st curve has been normalized by the average velocity? The equations are linear so the profile is the most interesting part.

-Peter
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Re: MHD: HARTMANN PROBLEM 2D

Post by Andrea_P »

Hi Peter,
Actually, the velocity is not normalized either in Paraview and in Matlab. If you have any other examples of this problem, could you share them, please? The most interesting part is when I will apply an electric field.
Regards,
Andrea
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Re: MHD: HARTMANN PROBLEM 2D

Post by Andrea_P »

Good Morning,
I have tried using a velocity of 0.5 m/s instead of 0.0015 m/s like in the previous problem. Unfortunately, the numeric and analytic solutions are quite different. I attached the solution. I am using Hartmann numbers very small to facilitate the convergence and the same case.sif. I attached the results. Thanks in advance for your answers.
Regards,
Andrea
Attachments
canale_2D_report_panchall.msh
(837.61 KiB) Downloaded 135 times
Numeric solution
Numeric solution
M=5.png (15.84 KiB) Viewed 47342 times
analytic solution
analytic solution
0.5.png (37.62 KiB) Viewed 47342 times
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