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The behavior of IAD_0 scheme, a fully conservative SPH scheme based on atensor formulation, is analyzed in connection with several astrophysicalscenarios, and compared to the same simulations carried out with the standardSPH technique. The proposed hydrodynamic scheme is validated using a variety ofnumerical tests that cover important topics in astrophysics, such as theevolution of supernova remnants, the stability of self-gravitating bodies andthe coalescence of compact objects. The results suggest that the SPH schemebuilt with the integral approach to the derivatives premise improves theresults of the standard SPH technique. In particular, it is observed a betterdevelopment of hydrodynamic instabilities, an improved description ofself-gravitant structures in equilibrium and a reasonable description of theprocess of coalescence of two white dwarfs. A good energy, and linear andangular momentum conservation, generally better than that of standard SPH, wasalso obtained. In addition the new scheme is less susceptible to suffer pairinginstability.

Testing the concept of integral approach to derivatives within the smoothed particle hydrodynamics technique in astrophysical scenarios