Numerical simulations of strong incompressible magnetohydrodynamic
  turbulence
  Magnetised plasma turbulence pervades the universe and is likely to play an
important role in a variety of astrophysical settings. Magnetohydrodynamics
(MHD) provides the simplest theoretical framework in which phenomenological
models for the turbulent dynamics can be built. Numerical simulations of MHD
turbulence are widely used to guide and test the theoretical predictions;
however, simulating MHD turbulence and accurately measuring its scaling
properties is far from straightforward. Computational power limits the
calculations to moderate Reynolds numbers and often simplifying assumptions are
made in order that a wider range of scales can be accessed. After describing
the theoretical predictions and the numerical approaches that are often
employed in studying strong incompressible MHD turbulence, we present the
findings of a series of high-resolution direct numerical simulations. We
discuss the effects that insufficiencies in the computational approach can have
on the solution and its physical interpretation.
