Accretion discs/Numerical simulations

The present understanding of black hole accretion rests on analytic models. Indeed, all the fundamental features of black hole accretion flows that have been recently calculated in terms of numerical simulations (including the most sophisticated 3D MHD simulations), were previously well understood in terms of analytic models. It seems that today, and in the foreseeable future, the super-computer simulations will keep confirming rather than solving or discovering. Today, the most important message of the supercomputer simulations of accretion discs seems to be that the approximations and simplifications adopted in the analytic models have been rather wisely chosen. Accretion discs can be treated either as a whole in global simulations or in parts with shearing box simulations. There are many numerical codes to solve the fluid equations in a relativistic and/or magneto-hydrodynamic environment: COSMOS ++ (Anninos et al, 2005), HARM (Gammie et al, 2003), RAISHIN (Mizuno et al, 2006) as well as codes developed by De Villiers & Hawley (2007), Komissarov (2004) and Anderson et al. (2006), just to name a few. Within these codes, different types of schemes are being used to treat discontinuities (shocks) in the flow. The artificial viscosity scheme (based on Wilson, 1977) and the Godunov scheme are primarily applied to work on relativistic accretion discs, but also schemes like smooth-particle hydrodynamics (SPH) and (pseudo-) spectral methods are considered. A detailed technical description of methods being used in numerical simulations of accretion discs may be found in the excellent (on line) Living Review by José A. Font, Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity. Hydrodynamical simulations of stationary discs Hydrodynamical simulations of non-stationary discs MHD 3D simulations of non-stationary discs MHD 3D simulations of non-stationary discs