  This paper investigates the hydrodynamic performances of an SPH code
incorporating an artificial heat conductivity term in which the adopted signal
velocity is applicable when gravity is present. In accordance with previous
findings it is shown that the performances of SPH to describe the development
of Kelvin-Helmholtz instabilities depend strongly on the consistency of the
initial condition set-up and on the leading error in the momentum equation due
to incomplete kernel sampling. An error and stability analysis shows that the
quartic B-spline kernel (M_5) possesses very good stability properties and we
propose its use with a large neighbor number, between ~50 (2D) to ~ 100 (3D),
to improve convergence in simulation results without being affected by the
so-called clumping instability. SPH simulations of the blob test show that in
the regime of strong supersonic flows an appropriate limiting condition, which
depends on the Prandtl number, must be imposed on the artificial conductivity
SPH coefficients in order to avoid an unphysical amount of heat diffusion.
Results from hydrodynamic simulations that include self-gravity show profiles
of hydrodynamic variables that are in much better agreement with those produced
using mesh-based codes. In particular, the final levels of core entropies in
cosmological simulations of galaxy clusters are consistent with those found
using AMR codes. Finally, results of the Rayleigh-Taylor instability test
demonstrate that in the regime of very subsonic flows the code has still
several difficulties in the treatment of hydrodynamic instabilities. These
problems being intrinsically due to the way in which in standard SPH gradients
are calculated and not to the implementation of the artificial conductivity
term.
