Re: [femm] Asymptotic boundary condition

[David Meeker <dmeeker@xxxxxxxxxxxxxxxxx>]

marco valcavi wrote:

> Hello
> I tried to make a simple simulation to verify the
> asymptotic b.c.
> I take a coil with a current and I simulate the B
> field at 1 m on axis (B1) and 90° off axis (B2). In
> the field produced by a dipole the ratio between B1
> and B2 should be 3 but with the mixed b.c. and the
> appropriate c0 I find that the ratio is nearly 2.
> I make an error somewhere?

A smoothing scheme is used in femm to smooth out the flux density which would
otherwise be piece-wise constant in each element. One of the points that you
examined (1 m on axis) is in a corner, where the smoothing scheme isn't so
accurate--not enough information to do really good smoothing. Flux density is
also less accurate on exterior boundaries than in the middle of the domain
(but not as bad as corners). You are just seeing areas where the smoothing
algorithm doesn't perform so great. If you want to turn off the smoothing
algorithm for comparison, you can do it by unchecking View|Smoothing from the
main menu of the post-processor.

At points that aren't right on the boundary, the field is as you might expect.
The field from a loop of current viewed from far enough away so that it looks
like a dipole is:

{Br,Bz} = {{(3*a*ni*r*uo*z)/(4*Pi*(r^2 + z^2)^(5/2)), -(a*ni*uo*(r^2 -
2*z^2))/(4*Pi*(r^2 + z^2)^(5/2))}}

where a is the loop's area, ni is the amp-turns carried by the loop, uo is the
permeability of free space.

For an example interior point, we could pick {0.6 m, 0.6 m}. At that point,
the program returns:
Br = 1.835e-006 Tesla
Bz = 6.192e-007 Tesla
if we take ni= 784.4017 and a=Pi*0.055^2 to match the problem geometry, the
analytical formula yields:
{1.830232623614073*^-6, 0, 6.10077541204691*^-7}
which seems like a reasonable match.

Dave.


begin:vcard 
n:Meeker;David
tel;fax:781-890-3489
tel;work:781-684-4070
x-mozilla-html:TRUE
url:http://www.foster-miller.com
org:Foster-Miller, Inc.;Electrical and Electronic Systems Group
adr:;;350 Second Avenue;Waltham;MA;02451;USA
version:2.1
email;internet:dmeeker@xxxxxxxxxxxxxxxxx
title:Senior Engineer
fn:David Meeker
end:vcard