Numerical models of black hole accretion flows

Black hole accretion flows are the hot, magnetized, turbulent plasma that surround black holes in astrophysical settings and in some cases make them the most luminous objects in the universe. I review recent developments in the numerical modeling of these plasmas. For weakly radiating flows it is now possible to follow the dynamics of the plasma by integrating the equations of general relativistic magnetohydrodynamics using numerical methods borrowed from nonrelativistic hydrodynamics. Ray tracing, along the curved trajectories followed by light close to the black hole event horizon, can then be used to create simulated observations of these weakly radiating flows. These models are relevant to the faint source at the galactic center, which may soon be directly imaged by millimeter interferometry.