We show that accretion disks , both in the subcritical and supercritical accretion rate regime , may exhibit significant amplitude luminosity oscillations .
The luminosity time behavior has been obtained by performing a set of time-dependent 2D SPH simulations of accretion disks with different values of \alpha 
and accretion rate .
In this study , to avoid any influence of the initial disk configuration , we produced the disks injecting matter from an outer edge far from the central object .
The period of oscillations is 2 - 50 s respectively for the two cases , and the variation amplitude of the disc luminosity is 10 ^ { 38 } - 10 ^ { 39 } erg/s .
An explanation of this luminosity behavior is proposed in terms of limit cycle instability : the disk oscillates between a radiation pressure dominated configuration ( with a high luminosity value ) and a gas pressure dominated one ( with a low luminosity value ) .
The origin of this instability is the difference between the heat produced by viscosity and the energy emitted as radiation from the disk surface ( the well-known thermal instability mechanism ) .
We support this hypothesis showing that the limit cycle behavior produces a sequence of collapsing and refilling states of the innermost disk region .