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Continuity Problem
Posted Oct 27, 2015, 2:38 p.m. EDT Low-Frequency Electromagnetics, Geometry 3 Replies
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Hello everyone,
I will appreciate if someone can help me with a doubt I have in Comsol. First, I will try to explain the situation:
I am trying to simulate the magnetic fields around the overhead transmission line considering the influence of the ground. In order to consider the hole region, I am using a mapping technique that maps an unbounded 2D space into a unit circle, in this case a point p(x,y) will be mapped to a unique point P(u,v). Considering that the ground surface is given at y = 0, I am mapping the space above the ground (y > 0) to a unit circle with center at (u = 0, v = 1), and the space below the ground (y < 0) to a unit circle with center at (u = 0, v = -1).
As you can see, the boundaries of both circles in the mapped domain are representing the ground surface, in other words, the boundary of the upper circle and the boundary of the lower circle are representing the same boundary (ground surface). For that reason, I want to make sure that I will have some kind of continuity with respect to the fields going through the boundaries. For example, if I have magnetic field going through the lower left side of the upper circle, then I should have a magnetic field coming out from the upper left side of the lower circle. I have attached a simple (silly) figure to help understanding how the upper and lower boundaries are related. In this figure, the boundaries with the same color are representing the same portion of the ground surface.
So, my question is, what condition should I use in these boundaries to ensure that they are the same boundary, even though these boundaries are physically separated.
Best regards,
Edison
I will appreciate if someone can help me with a doubt I have in Comsol. First, I will try to explain the situation:
I am trying to simulate the magnetic fields around the overhead transmission line considering the influence of the ground. In order to consider the hole region, I am using a mapping technique that maps an unbounded 2D space into a unit circle, in this case a point p(x,y) will be mapped to a unique point P(u,v). Considering that the ground surface is given at y = 0, I am mapping the space above the ground (y > 0) to a unit circle with center at (u = 0, v = 1), and the space below the ground (y < 0) to a unit circle with center at (u = 0, v = -1).
As you can see, the boundaries of both circles in the mapped domain are representing the ground surface, in other words, the boundary of the upper circle and the boundary of the lower circle are representing the same boundary (ground surface). For that reason, I want to make sure that I will have some kind of continuity with respect to the fields going through the boundaries. For example, if I have magnetic field going through the lower left side of the upper circle, then I should have a magnetic field coming out from the upper left side of the lower circle. I have attached a simple (silly) figure to help understanding how the upper and lower boundaries are related. In this figure, the boundaries with the same color are representing the same portion of the ground surface.
So, my question is, what condition should I use in these boundaries to ensure that they are the same boundary, even though these boundaries are physically separated.
Best regards,
Edison
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3 Replies Last Post Oct 29, 2015, 3:58 a.m. EDT
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Posted:
9 years ago
Hi. Although I'm not prepared to help you with your specific coordinate-mapping technique, I would like to suggest that this may be the sort of problem that you can actually solve just fine, especially in 2D, without resort to such a (conformal mapping?) transformation. In particular, you can zone your problem into two or more regions, using a relatively-fine mesh around the actual wire(s) in question, more and more coarser meshes farther away. You can actually put your outermost problem boundaries very far away using this approach, and then the boundary conditions you impose on those very-distant boundaries will become almost irrelevant, since the magnetic fields will become sufficiently weak there. So, for what it is worth, my approach would not be to try to apply any novel coordinate transformations, but rather to attack and solve the problem in its original real-world (or nearly real-world) geometry. Again, for a 2D problem, a reasonably decent modern computer will likely have all the speed and memory you'll need to do that using Comsol Multiphysics and the AC/DC module. That's just my humble opinion. Good luck.
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Posted:
9 years ago
Hi Robert, thanks for your response.
Actually, I don't have any problem with the mapping technique. I only want to make sure that I am applying the correct conditions to the boundaries, in order to make the upper circle boundaries as being the same as the lower circle boundaries, i.e., the boundaries of the upper circle have a continuity to their respective boundaries of the lower circle. (Not sure if I am being clear in this part)
I have done some simulation using truncation for a single wire over lossy ground for example, the problem is that at low frequencies, the skin depth of the ground can become comparable or even bigger than the truncation radius, forcing me to use even bigger truncation radius. That is why I wanted to map an unbounded (infinite) domain to a bounded domain (two circles with 1 m of radius).
Thanks again!
Actually, I don't have any problem with the mapping technique. I only want to make sure that I am applying the correct conditions to the boundaries, in order to make the upper circle boundaries as being the same as the lower circle boundaries, i.e., the boundaries of the upper circle have a continuity to their respective boundaries of the lower circle. (Not sure if I am being clear in this part)
I have done some simulation using truncation for a single wire over lossy ground for example, the problem is that at low frequencies, the skin depth of the ground can become comparable or even bigger than the truncation radius, forcing me to use even bigger truncation radius. That is why I wanted to map an unbounded (infinite) domain to a bounded domain (two circles with 1 m of radius).
Thanks again!
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Posted:
9 years ago
Hi,
If you want to map data form one place to another, you are looking for the General Extrusion coupling operator. Check out this informative blog post written by one of my colleagues: www.comsol.com/blogs/part-2-mapping-variables-with-general-extrusion-operators/
Regards,
Henrik
If you want to map data form one place to another, you are looking for the General Extrusion coupling operator. Check out this informative blog post written by one of my colleagues: www.comsol.com/blogs/part-2-mapping-variables-with-general-extrusion-operators/
Regards,
Henrik