  We discuss prospects of using multi-dimensional time-dependent simulations to
study the atmospheres of brown dwarfs and extrasolar giant planets, including
the processes of convection, radiation, dust formation, and rotation. We argue
that reasonably realistic simulations are feasible, however, separated into two
classes of local and global models. Numerical challenges are related to
potentially large dynamic ranges, and the treatment of scattering of radiation
in multi-D geometries.
