A novel computational hydrocode oriented to Astrophysical applications is described, discussed and validated in the following pages. The code, called SPHYNX, is of Newtonian type and grounded on the Euler-Lagrange formulation of the smoothed-particle hydrodynamics technique. The distinctive features of the code are: the use of an integral approach to estimating the gradients; the use of a flexible family of interpolators called sinc kernels, which suppress pairing instability; and the incorporation of a new type of volume elements which provides a better partition of the unity. The ensuing hydrodynamic code conserves mass, linear and angular momentum, energy, entropy and preserves kernel normalization even in strong shocks. By a careful choice of the index of the sinc kernel and the number of neighbors in the SPH summations, there is a substantial improvement in the estimation of gradients. Additionally, the new volume elements reduce the so-called tensile instability. Both features help to suppress much of the damp which often prevents the growth of hydrodynamic instabilities in regular SPH codes. On the whole, SPHYNX has passed the verification tests described below with excellent results. For identical particle setting and initial conditions the results were similar, and often better, than those obtained with other modern SPH schemes such as GADGET and PSPH, or with the recent density-independent formulation DISPH.
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