A Stable, Accurate Methodology for High Mach Number, Strong Magnetic   Field MHD Turbulence with Adaptive Mesh Refinement: Resolution and Refinement   Studies
  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. 
Pak Shing Li, Daniel F. Martin, Richard I. Klein, and Christopher F.   McKee
astro-ph.IM physics.comp-ph physics.flu-dyn