  The smoothed-particle hydrodynamics (SPH) technique is a numerical method for
solving gas-dynamical problems. It has been applied to simulate the evolution
of a wide variety of astrophysical systems. The method has a second-order
accuracy, with a resolution that is usually much higher in the compressed
regions than in the diluted zones of the fluid. In this work, we propose and
check a scheme to balance and equalize the resolution of SPH between high- and
low-density regions. This method relies on the versatility of a family of
interpolators called Sinc kernels, which allows increasing the interpolation
quality by varying only a single parameter (the exponent of the Sinc function).
The scheme is checked and validated through a number of numerical tests, from
standard one-dimensional Riemann problems in shock tubes, to multidimensional
simulations of explosions, hydrodynamic instabilities and the collapse of a
sun-like polytrope. The analysis of the hydrodynamical simulations suggests
that the scheme devised to equalizing accuracy improves the treatment of the
post-shock regions and, in general, of the rarefacted zones of fluids while
causing no harm to the growth of hydrodynamic instabilities. The method is
robust and easy to implement with a low computational overload. It conserves
mass, energy, and momentum and reduces to the standard SPH scheme in regions of
the fluid that have smooth density gradients.
