A divergence-cleaning scheme for cosmological SPMHD simulations
  In magnetohydrodynamics (MHD), the magnetic field is evolved by the induction
equation and coupled to the gas dynamics by the Lorentz force. We perform
numerical smoothed particle magnetohydrodynamics (Spmhd) simulations and study
the influence of a numerical magnetic divergence. For instabilities arising
from divergence B related errors, we find the hyperbolic/parabolic cleaning
scheme suggested by Dedner et al. 2002 to give good results and prevent
numerical artifacts from growing. Additionally, we demonstrate that certain
current Spmhd implementations of magnetic field regularizations give rise to
unphysical instabilities in long-time simulations. We also find this effect
when employing Euler potentials (divergenceless by definition), which are not
able to follow the winding-up process of magnetic field lines properly.
Furthermore, we present cosmological simulations of galaxy cluster formation at
extremely high resolution including the evolution of magnetic fields. We show
synthetic Faraday rotation maps and derive structure functions to compare them
with observations. Comparing all the simulations with and without divergence
cleaning, we are able to confirm the results of previous simulations performed
with the standard implementation of MHD in Spmhd at normal resolution. However,
at extremely high resolution, a cleaning scheme is needed to prevent the growth
of numerical errors at small scales.
