  We present a non-linear numerical model for a geometrically thin accretion
disk with the addition of stochastic non-linear fluctuations in the viscous
parameter. These numerical realizations attempt to study the stochastic effects
on the disk angular momentum transport. We show that this simple model is
capable of reproducing several observed phenomenologies of accretion driven
systems. The most notable of these is the observed linear rms-flux relationship
in the disk luminosity. This feature is not formally captured by the linearized
disk equations used in previous work. A Fourier analysis of the dissipation and
mass accretion rates across disk radii show coherence for frequencies below the
local viscous frequency. This is consistent with the coherence behavior
observed in astrophysical sources such as Cygnus X-1.
