SPMHD simulations of Structure Formation
  The intracluster medium of galaxy clusters is permeated by {\mu}G magnetic
fields. Observations with current and future facilities have the potential to
illuminate the role of these magnetic fields play in the astrophysical
processes of galaxy clusters. To obtain a greater understanding of how the
initial seed fields evolve to the magnetic fields in the intracluster medium
requires magnetohydrodynamic simulations. We critically assess the current
Smoothed Particle Magneto-Hydrodynamics (SPMHD) schemes, especially
highlighting the impact of a hyperbolic divergence cleaning scheme and
artificial resistivity switch on the magnetic field evolution in cosmological
simulations of the formation of a galaxy cluster using the N-body/SPMHD code
gcmhd++. The impact and performance of the cleaning scheme and two different
schemes for the artificial resistivity switch is demonstrated via idealized
test cases and cosmological simulations. We demonstrate that the hyperbolic
divergence cleaning scheme is effective at suppressing the growth of the
numerical divergence error of the magnetic field and should be applied to any
SPMHD simulation. Although the artificial resistivity is important in the
strong field regime, it can suppress the growth of the magnetic field in the
weak field regime, such as galaxy clusters. With sufficient resolution,
simulations with divergence cleaning can reproduce observed magnetic fields. We
conclude that the cleaning scheme alone is sufficient for galaxy cluster
simulations, but our results indicate that the SPMHD scheme must be carefully
chosen depending on the regime of the magnetic field.
