Smoothed particle hydrodynamics: checking a tensor approach to calculating gradients

We describe and check a novel formulation of Smoothed Particle Hydrodynamics (SPH) based on an Integral Approach to the Derivatives, called IAD_0, that can be applied to simulate astrophysical systems. The method relies in a tensor approach to calculating gradients, which is more accurate than the standard procedure (STD), due to its better renormalization properties. The proposed scheme fully conserves momentum and energy in isentropic flows, and is less susceptible to the pairing instability. The resulting algorithm is verified using two tests: a two-dimensional simulation of the Kelvin-Helmholtz instability and the three-dimensional simulation of the merging of two polytropes. The analysis of these test cases suggests that the method is able to improve the results of the standard technique with only a moderate computational overload.