I'm calculating the self inductance of a coil in a 2D setup by three methods (to compare them). First method is using the energy stored in the problem space which is reported by Elmer on the command line output (and in the save scalars output file). Then use L = (2 * Stored Magnetic Field Energy) / Current^2.
Second method is L = ( integral (Magnetic Vector Potential * Current Density) dV ) / current^2 where dV is over the volume of the conductor that forms the coil. In the case of a 2D cartesian problem, this is actually two bodies; one body has current flowing into the page and the other has current flowing out of the page. The turns of the coil are represented using the standard coil analytical approach in the circuits and dynamics module. The volume is taken care of by the value of the depth of the problem as passed to the circuits and dynamics module so we only need to worry about the area of the coil in the 2D setup. So we have L = integral (Magnetic Vector Potential * Current Density) dA (the current density is constant as a function of depth and so is the magnetic vector potential as they are solved on a mesh which is a 2D plane).
Third method is to place a lumped resistance (using the circuits and dynamics module) in series with the FE modelled coil and impose a square wave voltage having a period which is long compared to the expected time constant of the inductor + resistor circuit. The exponential rise of the current can be used with the value of the resistance to work out the inductance. Of course being careful not to saturate the core material as inductance (as in a fixed value for a given coil and core) is a concept that only makes sense in linear systems.
My question is can I get with save scalars to do the integral in the second method? I can have it output the integral of A over the masked area (coil portion 1 and separately coil portion 2) and I can ask it for the integral of the current density over the two masked regions as well. I have been unable, so far, to ask it to produce the integral of the product of A and J. I suspect there will be some method with MATC that will achieve what I'd like to but, I don't know where to look for the details.
General discussion about Elmer
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