  Numerical MHD codes have become extraordinarily powerful tools with which to study accretion turbulence. They have been used primarily to extract values for the classical $\alpha$ parameter, and to follow complex evolutionary development. Energy transport, which is at the heart of classical disk theory, has yet to be explored in any detail. Further topics that should be explored by simulation include nonideal MHD, radiation physics, and outburst behavior related to the temperature sensitivity of the resistivity. 
Numerical Simulations of the MRI and Real Disks