  In this era of precision cosmology, a detailed physical understanding on the
evolution of cosmic baryons is required. Cosmic magnetic fields, though still
poorly understood, may represent an important component in the global cosmic
energy flow that affects the baryon dynamics. We have developed an
Eulerian-based cosmological magnetohydrodynamics code (CosmoMHD) with modern
shock capturing schemes to study the formation and evolution of cosmic
structures in the presence of magnetic fields. The code solves the ideal MHD
equations as well as the non-equilibrium rate equations for multiple species,
the Vlasov equation for dynamics of collisionless particles, the Poisson's
equation for the gravitational potential field and the equation for the
evolution of the intergalactic ionizing radiation field. In addition, a
detailed star formation prescription and feedback processes are implemented.
Several methods for solving the MHD by high-resolution schemes with
finite-volume and finite-difference methods are implemented. The
divergence-free condition of the magnetic fields is preserved at a level of
computer roundoff error via the constraint transport method. We have also
implemented a high-resolution method via dual-equation formulations to track
the thermal energy accurately in very high Mach number or high Alfven-Mach
number regions. Several numerical tests have demonstrated the efficacy of the
proposed schemes.
