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The reduction of V in Ampere's law in time-dependent 3D mf
Posted 20.06.2020, 09:19 GMT-4 Electromagnetics, Low-Frequency Electromagnetics 1 Reply
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Hello everyone. I am generally working on 3D transient magnetic field solution in COMSOL. The A formulation that COMSOL used for 3D mf module Ampere law is:
The right side of the equations is the source side, and this is done by current excitations/lumped ports, etc. The defined lumped port between conductors creates 
field, which ensures the targeted current in the closed-loop. (again this is my understanding from the user manuals and applications notes).
Thus, the generated is used to update 
as in
. Then the Ampere law in the conductor domain becomes only dependent and this is the equation of COMSOL 3d mf module form.
However, I believe that the way that field should be constructed as in
which introduces a new variable rather than magnetic vector potential. In the literature, (most of them the methodologies of 3D eddy current modeling with FEM in Transaction on Magnetics in '80s and early '90s), 
(reduced electrical scalar potential) term can be reduced to zero in the case of the conductivity of the material homogeneous. In the case of non-uniform conductivity/or in different conductor contact case the continuity of tangential does not ensure the continuity of which can be problematic. Of course, A-V formulation can be introduced, but this is not the case for 3D transient mf, I believe. The question I want to ask is the Comsol's ampere law reduced V term with the assumption that the conductivity of the domain is uniform. To be clear, when I change the conductivity of the material for some modeling purposes (making it time-position dependent), the solution of the A field distribution has an error due to the lack of V term? Or COMSOL makes a different technique to reduce the V term in Ampere's law?
Sincerely,
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If you find a good source of explanation about this I would be interested.
I had a similar difficulty, working with Poisson equation in transient condition and with 
being non-uniform. I believe your situation is symmetrical, although I have not tried to check your math.
I was able to convince myself through scaling arguments that for the additional term to matter, charge carriers had to move at a speed similar to the speed of light. Since charges in my system move many order of magnitudes slower than this, I felt confident discarding the term.
Perhaps a similar argument applies to your case?