[Getdp] Erroneous interaction between constraints

[DILASSER Guillaume]

Dear GetDP community,

I am facing a problem with the implementation of constraints in a magnetodynamical model : I basically have two constraints to enforce and they interact badly in a way that is almost unpredictable, causing erroneous results. First, I enclose with this mail a schematics to explain the problem. To simplify, I am considering one fourth of the cross-section (the top-right part) of a dipole in 2D. I have a conducting domain that is carrying a known current I in the Z-direction (note that the current density itself is not set). There is a symmetry with the X-axis, the lower-right corner should also have a conductor carrying I, and with the Y-axis, the top-left and bottom-left corner having each a conductor with a -I current.

To achieve this, I am using the H-Phi formulation and I use two separate constraints :

·         One on the current flowing through the upper-right conductor. This is done by generating à cut in the air with the Cohomology module, then I create a DoF on it and constraining it to be my total current.

·         Second is a Phi = cst condition on the X-axis to generate the mirror symmetry.
However, Cohomology generates its edge chain randomly and when it hits the X-axis, then the two constraints interact badly and mess the solution up. If I understand well, in this case, Phi should be equal to a constant on the elements of the X-axis on one side of the cohomology cut and another constant on the other side, with the difference between the constants being the Jump in Phi over the cut. Am I correct with this ?

I know that an option to circumvent the problem would be to model half of the windings instead of one fourth like I am doing now. By modeling the complete right side for example, I would get rid of the boundary condition on the X-axis and thus of the problem. However, this also mean doubling the size of my model and I would like to avoid it if possible. Thus, I would like to know if someone knows how I could change the implementation of my constraints to get the correct effect. Your help would be greatly appreciated.

Sincerely yours,

Guillaume DILASSER
Doctorant SACM / LEAS
CEA - Centre de Saclay - Bât.123 - PC 319c
91191 Gif sur Yvette Cedex - France -

guillaume.dilasser at cea.fr<mailto:guillaume.dilasser at cea.fr>

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