Eddy Current solver

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Ed­dy cur­rents (al­so called Fou­cault cur­rents) are cur­rents in­duced in con­duc­tors, when a con­duc­tor is ex­posed to a chang­ing mag­net­ic field due to rel­a­tive mo­tion of the field source and con­duc­tor; or due to vari­a­tions of the field with time. This caus­es a cir­cu­lat­ing flow of elec­trons, or a cur­rent, with­in the body of the con­duc­tor. These cir­cu­lat­ing ed­dies of cur­rent then in­duce mag­net­ic fields. These fields gen­er­ate a force called the Lorentz force that can cause re­pul­sive, at­trac­tive, propul­sion and drag ef­fects. The stronger the ap­plied mag­net­ic field,  or the faster the field changes, then the greater the cur­rents that are de­vel­oped and the greater the fields pro­duced.

The Ed­dy cur­rent solver avail­able in the elec­tro­mag­net­ism mod­ule al­lows to solve prob­lems in the so-called “ed­dy-cur­rent” ap­prox­i­ma­tion, which is valid for good enough con­duc­tors with low fre­quen­cy vary­ing fields such that the dis­place­ment cur­rents can be ne­glect­ed com­pared to the cur­rent den­si­ty. This ap­prox­i­ma­tion im­plies a di­ver­gence free cur­rent den­si­ty and no free charge ac­cu­mu­la­tion (see Maxwell equa­tions). Some of the in­dus­tri­al ap­pli­ca­tions in­volve elec­tric met­al form­ing, met­al cut­ting, met­al weld­ing or high mag­net­ic pres­sure gen­er­a­tion. The Joule heat­ing is al­so tak­en in­to ac­count for cou­pling with the LS-DY­NA ther­mal solver.

The Maxwell equa­tions are solved us­ing a Fi­nite El­e­ment Method (FEM) for the sol­id con­duc­tors cou­pled with a Bound­ary El­e­ment Method (BEM) for the sur­round­ing air (or in­su­la­tors). Thus, no air mesh is nec­es­sary.