  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.
