  In galaxy clusters, modern radio interferometers observe non-thermal radio
sources with unprecedented spatial and spectral resolution. For the first time,
the new data allows to infer the structure of the intra-cluster magnetic fields
on small scales via Faraday tomography. This leap forward demands new numerical
models for the amplification of magnetic fields in cosmic structure formation -
the cosmological magnetic dynamo. Here we present a novel numerical approach to
astrophyiscal MHD simulations aimed to resolve this small-scale dynamo in
future cosmological simulations. As a first step, we implement a fifth order
WENO scheme in the new code WOMBAT. We show that this scheme doubles the
effective resolution of the simulation and is thus less expensive than common
second order schemes. WOMBAT uses a novel approach to parallelization and load
balancing developed in collaboration with performance engineers at Cray Inc.
This will allow us scale simulation to the exaflop regime and achieve kpc
resolution in future cosmological simulations of galaxy clusters. Here we
demonstrate the excellent scaling properties of the code and argue that
resolved simulations of the cosmological small scale dynamo within the whole
virial radius are possible in the next years.
