  Despite greatly improved observational methods, the presence of magnetic
fields at cosmological scales and their role in the process of large-scale
structure formation still remains unclear. In this paper we want to address the
question how the presence of a hypothetical primordial magnetic field on large
scales influences the cosmic structure formation in numerical simulations. As a
tool for carrying out such simulations, we present our new numerical code
AMIGA. It combines an N-body code with an Eulerian grid-based solver for the
full set of MHD equations in order to conduct simulations of dark matter,
baryons and magnetic fields in a self-consistent way in a fully cosmological
setting. Our numerical scheme includes effective methodes to ensure proper
capturing of shocks and highly supersonic flows and a divergence-free magnetic
field. The high accuracy of the code is demonstrated by a number of numerical
tests. We then present a series of cosmological MHD simulations and confirm
that, in order to have a significant effect on the distribution of matter on
large scales, the primordial magnetic field strength would have to be
significantly higher than the current observational and theoretical
constraints.
