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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 remain 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 magnetohydrodynamics (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 methods 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.

Investigating the influence of magnetic fields upon structure formation with amiga – a c code for cosmological magnetohydrodynamics