  In this paper we present results from a series of hydrodynamical tests aimed
at validating the performance of a smoothed particle hydrodynamics (SPH)
formulation in which gradients are derived from an integral approach. We
specifically investigate the code behavior with subsonic flows, where it is
well known that zeroth-order inconsistencies present in standard SPH make it
particularly problematic to correctly model the fluid dynamics. In particular
we consider the Gresho-Chan vortex problem, the growth of Kelvin-Helmholtz
instabilities, the statistics of driven subsonic turbulence and the cold
Keplerian disc problem. We compare simulation results for the different tests
with those obtained, for the same initial conditions, using standard SPH. We
also compare the results with the corresponding ones obtained previously with
other numerical methods, such as codes based on a moving-mesh scheme or
Godunov-type Lagrangian meshless methods. We quantify code performances by
introducing error norms and spectral properties of the particle distribution,
in a way similar to what was done in other works. We find that the new SPH
formulation exhibits strongly reduced gradient errors and outperforms standard
SPH in all of the tests considered. In fact, in terms of accuracy we find good
agreement between the simulation results of the new scheme and those produced
using other recently proposed numerical schemes. These findings suggest that
the proposed method can be successfully applied for many astrophysical problems
in which the presence of subsonic flows previously limited the use of SPH, with
the new scheme now being competitive in these regimes with other numerical
methods.
