Adaptative Smooth Particle Hydrodynamics and Particle-Particle coupled codes: Energy and Entropy Conservation

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.