  We present a series of 2-dimensional hydrodynamic simulations of massive
disks around protostars. We simulate the same physical problem using both a
`Piecewise Parabolic Method' (PPM) code and a `Smoothed Particle Hydrodynamic'
(SPH) code, and analyze their differences. The disks studied here range in mass
from $0.05 M_*$ to $1.0 M_*$ and in initial minimum Toomre $Q$ value from 1.1
to 3.0. For this problem, the strengths of the codes overlap only in a limited
fashion, but similarities exist in their predictions, including spiral arm
pattern speeds and morphological features. Our results represent limiting cases
(i.e. systems evolved isothermally) rather than true physical systems. Disks
become active from the inner regions outward. From the earliest times, their
evolution is a strongly dynamic process rather than a smooth progression toward
eventual nonlinear behavior. We calculate approximate growth rates for the
spiral patterns; the one-armed ($m=1$) spiral arm is not the fastest growing
pattern of most disks. In our SPH simulations, disks with initial minimum
$Q=1.5$ or lower break up into proto-binary or proto-planetary clumps. However,
these simulations cannot follow the physics important for the flow and must be
terminated before the system has completely evolved. At their termination, PPM
simulations with similar initial conditions show uneven mass distributions
within spiral arms, suggesting that clumping behavior might result if they were
carried further. Concern that the point-like nature of SPH exaggerates
clumping, that our representation of the gravitational potential in PPM is too
coarse, and that our physics assumptions are too simple, suggest caution in
interpretation of the clumping in both the disk and torus simulations.
