Numerical Simulations Of Advective Flows Around Black Holes
  We present fully time-dependent solutions of accretion processes on black holes and compare them with analytical solutions. We use Smoothed Particle Hydrodynamics and Total Variation Diminishing mathods as the numerical tenchniques. Apart from steady state solutions, we also obtain time dependent results where the shock oscillates with the characteristic period of quasi-periodic oscillations (QPOs) observed in galactic and extragalactic black hole candidates. This oscillation produces 10-15% variation in the hard X-rays in galactic candidates and in soft X-rays in Extragalactic candidates. 
Sandip K. Chakrabarti, D. Ryu, D. Molteni, H. Sponholz, G. Lanzafame,   G. Eggum