  Performing a stable, long duration simulation of driven MHD turbulence with a
high thermal Mach number and a strong initial magnetic field is a challenge to
high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing
positivity of the density and pressure. We have implemented a robust
combination of reconstruction schemes, Riemann solvers, limiters, and
Constrained Transport EMF averaging schemes that can meet this challenge, and
using this strategy, we have developed a new Adaptive Mesh Refinement (AMR) MHD
module of the ORION2 code. We investigate the effects of AMR on several
statistical properties of a turbulent ideal MHD system with a thermal Mach
number of 10 and a plasma $\beta_0$ of 0.1 as initial conditions; our code is
shown to be stable for simulations with higher Mach numbers ($M_rms = 17.3$)
and smaller plasma beta ($\beta_0 = 0.0067$) as well. Our results show that the
quality of the turbulence simulation is generally related to the
volume-averaged refinement. Our AMR simulations show that the turbulent
dissipation coefficient for supersonic MHD turbulence is about 0.5, in
agreement with unigrid simulations.
