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Periodic boundary conditions in a torus (donut)

Posted Nov 10, 2010, 1:30 p.m. EST Low-Frequency Electromagnetics, Geometry, Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers Version 4.1 5 Replies

Nicholas Eidietis
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I have a 3-D torus (donut) centered around the y axis. The vector field that I am solving for ([Ux Uy Uz]) is periodic every 5 degrees in the toroidal direction, so I would obviously like to model only a 5 degree section of the torus.

Mathematically, what I need to do is set up the boundary conditions with rotation:

U2 = [ cos(a) 1 -sin(a)
0 1 0
sin(a) 1 cos(a)] * U1

where a is the angle of my periodicity (5 degrees), U1 is the vector field on the 0-degree boundary, and U2 is the vector field on the 5-degree boundary.

I have set this up in "Periodic Boundary Conditions", but I cannot seem to get it to work. I contacted COMSOL support, and they said that it was not possible to implement such a boundary condition (essentially a rotated continuity condition). That does not seem correct to me... this seems like a pretty trivial boundary condition.

So I ask this question of the community: Is it possible to implement this boundary condition, or do I have to use the full 3-D model with its 360/5=72 fold redundancy?

Comsol 3.5a

Thanks,
Nick
5 Replies Last Post Oct 7, 2011, 8:27 a.m. EDT
George Hwang
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Posted: 1 decade ago Nov 29, 2010, 12:56 a.m. EST
Hi Nick,

I have been trying to do almost the exact same problem but have not had any luck. I too feel like there must be a way to model a section (or turn) of the toroid rather than the whole structure. And like you I have been trying to implement it with periodic boundary conditions and extrusion coupling but have not got it to work.

Have you had any luck? Any insight that you can share?

Thanks,
George
Hi Nick, I have been trying to do almost the exact same problem but have not had any luck. I too feel like there must be a way to model a section (or turn) of the toroid rather than the whole structure. And like you I have been trying to implement it with periodic boundary conditions and extrusion coupling but have not got it to work. Have you had any luck? Any insight that you can share? Thanks, George
Nicholas Eidietis
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Posted: 1 decade ago Nov 29, 2010, 12:48 p.m. EST
Hi George,

I did make a bit of progress on this. After some more discussions with the Comsol staff, I ended up using boundary extrusion coupling variables to make the toroidal periodicity that I wanted.

Here is the general idea:

(1) Create a geometry that includes 2 periods in your torus

(2) Embed a 2D plane in the middle of that 3D geometry (between the first and second period) in order to have access to an internal boundary plane

(3) In the boundary extrusion coupling variables menu, select the middle boundaries as your source and create extrusion variables with the necessary rotation. Select the two end boundaries as your destination.

(4) In physics->boundary conditions, set the toroidal boundaries of the torus to your extrusion coupling variables. In my case I was interested in the magnetic vector potential, so I set the boundary condition to "Magnetic Vector Potential" and then set the values equal to my extrusion coupling variables.

Hope this makes sense. I do not know if this is the most elegant solution, and it does require 2 periods, but it is a lot better than building the whole torus. It seems to work for me. Let me know if you need a clearer explanation.

Nick
Hi George, I did make a bit of progress on this. After some more discussions with the Comsol staff, I ended up using boundary extrusion coupling variables to make the toroidal periodicity that I wanted. Here is the general idea: (1) Create a geometry that includes 2 periods in your torus (2) Embed a 2D plane in the middle of that 3D geometry (between the first and second period) in order to have access to an internal boundary plane (3) In the boundary extrusion coupling variables menu, select the middle boundaries as your source and create extrusion variables with the necessary rotation. Select the two end boundaries as your destination. (4) In physics->boundary conditions, set the toroidal boundaries of the torus to your extrusion coupling variables. In my case I was interested in the magnetic vector potential, so I set the boundary condition to "Magnetic Vector Potential" and then set the values equal to my extrusion coupling variables. Hope this makes sense. I do not know if this is the most elegant solution, and it does require 2 periods, but it is a lot better than building the whole torus. It seems to work for me. Let me know if you need a clearer explanation. Nick
George Hwang
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Posted: 1 decade ago Nov 30, 2010, 3:11 p.m. EST
Hi Nick,

Thanks for the detailed tips. I have one more question regarding a 3D toroid.

How do you set an exciting input current into such a system for the two turns? You do not have access to the the turn boundaries because they are set as "Magnetic Potential" boundary extrusion couplings.

Thanks,
George
Hi Nick, Thanks for the detailed tips. I have one more question regarding a 3D toroid. How do you set an exciting input current into such a system for the two turns? You do not have access to the the turn boundaries because they are set as "Magnetic Potential" boundary extrusion couplings. Thanks, George
brockap3
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Posted: 1 decade ago Aug 25, 2011, 12:32 p.m. EDT
Hi, I would like to understand this as well. I am creating something of a toroidal inductor and would like to model only a section (or I guess 2 as you stated) to reduce the load on memory and such. I have done what you suggested up to step 3. This is where i get lost. Where exactly do you find this "boundary extrusion coupling variables" menu? And how do you go about creating these extrusion variables. Thanks for the help ahead of time.

~Brock
Hi, I would like to understand this as well. I am creating something of a toroidal inductor and would like to model only a section (or I guess 2 as you stated) to reduce the load on memory and such. I have done what you suggested up to step 3. This is where i get lost. Where exactly do you find this "boundary extrusion coupling variables" menu? And how do you go about creating these extrusion variables. Thanks for the help ahead of time. ~Brock
Bakkaoui Otmane
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Posted: 1 decade ago Oct 7, 2011, 8:27 a.m. EDT
I have one structure, and i want to calculate the repetion of this structure on one metter, in this case, how can I use periodicity
I have one structure, and i want to calculate the repetion of this structure on one metter, in this case, how can I use periodicity

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