  The behavior of IAD_0 scheme, a fully conservative SPH scheme based on a
tensor formulation, is analyzed in connection with several astrophysical
scenarios, and compared to the same simulations carried out with the standard
SPH technique. The proposed hydrodynamic scheme is validated using a variety of
numerical tests that cover important topics in astrophysics, such as the
evolution of supernova remnants, the stability of self-gravitating bodies and
the coalescence of compact objects. The results suggest that the SPH scheme
built with the integral approach to the derivatives premise improves the
results of the standard SPH technique. In particular, it is observed a better
development of hydrodynamic instabilities, an improved description of
self-gravitant structures in equilibrium and a reasonable description of the
process of coalescence of two white dwarfs. A good energy, and linear and
angular momentum conservation, generally better than that of standard SPH, was
also obtained. In addition the new scheme is less susceptible to suffer pairing
instability.
