Cosmological AMR MHD with Enzo
  In this work, we present MHDEnzo, the extension of the cosmological code Enzo
to include the effects magnetic fields through the ideal MHD approximation. We
use a higher order Godunov Riemann solver for the computation of interface
fluxes. We use two constrained transport methods to compute the electric field
from those interface fluxes, which simultaneously advances the induction
equation and maintains the divergence of the magnetic field. A third order
divergence free reconstruction technique is used to interpolate the magnetic
fields in the block structured AMR framework already extant in Enzo. This
reconstruction also preserves the divergence of the magnetic field to machine
precision. We use operator splitting to include gravity and cosmological
expansion. We then present a series of cosmological and non cosmological tests
problems to demonstrate the quality of solution resulting from this combination
of solvers.
