A new Finite Element Method for magnetodynamical problems : two-dimensional results

Caroline  Nore, LIMSI-CNRS & Universite Paris 11, Orsay

A mixed Lagrange finite element technique
    to solve the Maxwell equations in the magneto-hydrodynamic (MHD) limit
    in an hybrid domain composed of vacuum and conducting regions is presented.
    The originality of the approach is that no artificial
    boundary condition is enforced at the interface between the
    conducting and the insulating regions and the
    non-conducting medium is not approximated by
    a weakly conducting medium as is frequently done in the literature.
    As a first evaluation of the performance of the method,
    we study two-dimensional (2D) configurations,
    where the flow streamlines of the conducting fluid
    are planar, {\em i.e.} invariant in one direction, and
    either the magnetic field ("magnetic scalar" case)
    or the electric field ("electric scalar" case) is parallel to the invariant
    direction. Induction heating, eddy current
    generation, and magnetic field stretching are investigated showing the
    usefulness of finite element methods to solve magneto-dynamical
    problems with complex insulating boundaries.