  We present and test a general-purpose code, called PPASPH, for evolving
self-gravitating fluids in astrophysics, both with and without a collisionless
component. In PPASPH, hydrodynamical properties are computed by using the SPH
(Smoothed Particle Hydrodynamics) method while, unlike most previous
implementations of SPH, gravitational forces are computed by a PP
(Particle-Particle) approach. another important feature of this code is that
hydrodynamics equations optionally include the correction terms appearing when
$h(t,\br)$ is not constant. Our code has been implemented by using the data
parallel programming model on CM5(CM). PPASPH has been applied to study the
importance of adaptative smoothing correction terms on the entropy
conservation. We confirm Hernquist's (1993) interpretation of the entropy
violation observed in previous SPH simulations as a result of having neglected
these terms. An improvement on the entropy conservation is not found by merely
considering larger numbers of particles or different $N_S$ choices. The correct
continuum description is only obtained if the $\bn h$ correction terms are
included. Otherwise, the entropy conservation is always rather poor as compared
to that found for the total energy.
