  Black holes (BHs) surrounded by accretion disks are present in the Universe
at different scales of masses, from microquasars up to the active galactic
nuclei (AGNs). The current picture remains ad hoc due to the complexity of the
magnetic field action. In addition, accretion disks at high Eddington rates can
be radiation-pressure dominated and, according to some of the heating
prescriptions, thermally unstable. The observational verification of their
resulting variability patterns may shed light on both the role of radiation
pressure and magnetic fields. We compute the structure and time evolution of an
accretion disk, using the code GLADIS (which models the global accretion disk
instability). We supplement this model with a modified viscosity prescription,
which can to some extent describe the magnetisation of the disk. We study the
results for a large grid of models, to cover the whole parameter space, and we
derive conclusions separately for different scales of black hole masses, which
are characteristic for various types of cosmic sources. We show the
dependencies between the flare or outburst duration, its amplitude, and period,
on the accretion rate and viscosity scaling. We show that if the heating rate
in the accretion disk grows more rapidly with the total pressure and
temperature, the instability results in longer and sharper flares. In general,
we confirm that the disks around the supermassive black holes are more
radiation-pressure dominated and present relatively brighter bursts. Our method
can also be used as an independent tool for the black hole mass determination,
which we confront now for the intermediate black hole in the source HLX-1.
