  Massive stars can during their evolution reach the phase of critical (or very
rapid, near-critical) rotation when further increase in rotation rate is no
longer kinematically allowed. The mass ejection and angular momentum outward
transport from such rapidly rotating star's equatorial surface may lead to
formation and supports further existence of a circumstellar outflowing (stellar
decretion) disk. The efficient mechanism for the outward transport of the mass
and angular momentum is provided by the anomalous viscosity. The outer
supersonic regions of the disks can extend up to a significantly large distance
from the parent star, the exact radial extension is however basically unknown,
partly due to the uncertainties in radial variations of temperature and
viscosity.
  We study in detail the behavior of hydrodynamic quantities, i.e., the
evolution of density, radial and azimuthal velocity, and angular momentum loss
rate in stellar decretion disks out to extremely distant regions. We
investigate the dependence of these physical characteristics on the
distribution of temperature and viscosity. We also study the magnetorotational
instability, which we regard to be the source of anomalous viscosity in such
outflowing disks and to some extent we provide the preliminary models of the
two-dimensional radially-vertically correlated distribution of the disk density
and temperature.
  We developed our own two-dimensional hydrodynamic and magnetohydrodynamic
numerical code based on an explicit Eulerian finite difference scheme on
staggered grid, including full Navier-Stokes viscosity. We use semianalytic
approach to investigate the radial profile of magnetorotational instability,
where on the base of the numerical time-dependent hydrodynamic model we
analytically study the stability of outflowing disks submerged to the magnetic
field of central star.
