  We present a set of global, self-consistent N-body/SPH simulations of the
dynamic evolution of galactic discs with gas and including magnetic fields. We
have implemented a description to follow the evolution of magnetic fields with
the ideal induction equation in the SPH part of the Vine code. Results from a
direct implementation of the field equations are compared to a representation
by Euler potentials, which pose a div(B)-free description, an constraint not
fulfilled for the direct implementation. All simulations are compared to an
implementation of magnetic fields in the Gadget code which includes also
cleaning methods for div(B).
  Starting with a homogeneous seed field we find that by differential rotation
and spiral structure formation of the disc the field is amplified by one order
of magnitude within five rotation periods of the disc. The amplification is
stronger for higher numerical resolution. Moreover, we find a tight connection
of the magnetic field structure to the density pattern of the galaxy in our
simulations, with the magnetic field lines being aligned with the developing
spiral pattern of the gas. Our simulations clearly show the importance of
non-axisymmetry for the evolution of the magnetic field.
