Improving the thin-disk models of circumstellar disk evolution. The
  2+1-dimensional model
  Circumstellar disks of gas and dust are naturally formed from contracting
pre-stellar molecular cores during the star formation process. To study various
dynamical and chemical processes that take place in circumstellar disks prior
to their dissipation and transition to debris disks, the appropriate numerical
models capable of studying the long-term disk chemodynamical evolution are
required. We present a new 2+1-dimensional numerical hydrodynamics model of
circumstellar disk evolution, in which the thin-disk model is complemented with
the procedure for calculating the vertical distributions of gas volume density
and temperature in the disk. The reconstruction of the disk vertical structure
is performed at every time step via the solution of the time-dependent
radiative transfer equations coupled to the equation of the vertical
hydrostatic equilibrium. We perform a detailed comparison between circumstellar
disks produced with our previous 2D model and with the improved 2+1D approach.
The structure and evolution of resulting disks, including the differences in
temperatures, densities, disk masses and protostellar accretion rates, are
discussed in detail. The new 2+1D model yields systematically colder disks,
while the in-falling parental clouds are warmer. Both effects act to increase
the strength of disk gravitational instability and, as a result, the number of
gravitationally bound fragments that form in the disk via gravitational
fragmentation as compared to the purely 2D thin-disk simulations with a
simplified thermal balance calculation.
