  We have developed a parallel, simple, and fast hydrodynamics code for
multi-dimensional, self-gravitating, adiabatic flows. Our primary motivation is
the study of the non-linear evolution of white dwarf oscillations excited via
tidal resonances, typically over hundreds of stellar dynamical times.
Consequently, we require long term stability, low diffusivity, and high
algorithmic efficiency. An explicit, Eulerian, finite-difference scheme on a
regular Cartesian grid fulfills these requirements. It provides uniform
resolution throughout the flow, as well as simplifying the computation of the
self-gravitational potential, which is done via spectral methods. In this
paper, we describe the numerical scheme and present the results of some
diagnostic problems. We also demonstrate the stability of a cold white dwarf in
three dimensions over hundreds of dynamical times. Finally, we compare the
results of the numerical scheme to the linear theory of adiabatic oscillations,
finding numerical quality factors on the order of 6000, and excellent agreement
with the oscillation frequency obtained by the linear analysis.
