Simulating Supersonic Turbulence in Magnetized Molecular Clouds
  We present results of large-scale three-dimensional simulations of weakly
magnetized supersonic turbulence at grid resolutions up to 1024^3 cells. Our
numerical experiments are carried out with the Piecewise Parabolic Method on a
Local Stencil and assume an isothermal equation of state. The turbulence is
driven by a large-scale isotropic solenoidal force in a periodic computational
domain and fully develops in a few flow crossing times. We then evolve the flow
for a number of flow crossing times and analyze various statistical properties
of the saturated turbulent state. We show that the energy transfer rate in the
inertial range of scales is surprisingly close to a constant, indicating that
Kolmogorov's phenomenology for incompressible turbulence can be extended to
magnetized supersonic flows. We also discuss numerical dissipation effects and
convergence of different turbulence diagnostics as grid resolution refines from
256^3 to 1024^3 cells.
