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We present a series of 2-dimensional hydrodynamic simulations of massive disks around protostars using the PROMETHEUS 'Piecewise Parabolic Method' (PPM) based code. These simulations model disks of mass $0.1M_{\sun} \leq M_D \leq 1M_{\sun}$ and are characterized by a minimum Toomre Q value of $Q=1.5$. Power laws similar to those used by Adams, Ruden and Shu (1989) are adopted for the initial density and temperature in the disk and the central star ($M_*=1M_{\sun}$) is free to move in response to growing perturbations. Although no initial perturbation in the disk is assumed, instability is thought to be seeded by a combination of two factors. First, the grid forces the disk to be cut off in the radial direction at a distance large compared to the solar radius, creating a gravitational potential ``hump'' for the star to roll off of. Second, the density law is cut off near the inner radial boundary in order to avoid non-physical effects of matter running into the boundary. This creates a region of high `vortensity' in the inner region which is found to have instability modes of it's own by Papaloizou and Lin (1989). Starting from only these factors, growth of non-axisymmetric instabilities (spiral arms) is observed to occur over dynamical time scales of the disk. Growth constants are derived for the various modes present. Additionally, short duration oscillation in the amplitude of these spiral arms is observed and is attributed to fragmentation and reformation of arms as evolution progresses. A comparison is made between the behavior of a representative problem using the PROMETHEUS code and the Smoothed Particle Hydrodynamic (SPH) code.
