  We present 2D, ideal-MHD numerical simulations of the Parker instability in a
multi-component warm disk model. The calculations were done using two numerical
codes with different algorithms, TVD and ZEUS-3D. The outcome of the numerical
experiments performed with both codes is very similar, and confirms the results
of the linear analysis for the undular mode derived by Kim et al. (2000): the
most unstable wavelength is about 3 kpc and its growth timescale is between
30-50 Myr (the growth rate is sensitive to the position of the upper boundary
of the numerical grid). Thus, the time and length scales of this multicomponent
disk model are substantially larger than those derived for thin disk models. We
use three different types of perturbations, random, symmetric, and
antisymmetric, to trigger the instability. The antisymmetric mode is dominant,
and determines the minimum time for the onset of the nonlinear regime. The
instability generates dense condensations and the final peak column density
value in the antisymmetric case, as also derived by Kim et al. (2000), is about
a factor of 3 larger than its initial value. These wavelengths and density
enhancement factors indicate that the instability alone cannot be the main
formation mechanism of giant molecular clouds in the general interstellar
medium. The role of the instability in the formation of large-scale
corrugations along spiral arms is briefly discussed.
