Numerical Simulations of MHD turbulence in accretion disks

We review numerical simulations of MHD turbulence. The last decade has witnessed fundamental advances both in the technical capabilities of direct numerical simulation, and in our understanding of key physical processes. Magnetic fields tap directly into the free energy sources in a sufficiently ionized gas. The result is that adverse angular velocity and adverse temperature gradients, not the classical angular momentum and entropy gradients, destabilize laminar and stratified flow. This has profound consequences for astrophysical accretion flows, and has opened the door to a new era of numerical simulation experiments.