A one-parameter family of interpolating kernels for smoothed particle hydrodynamics studies

A set of interpolating functions of the type f ( v ) = { sin π 2 v / π 2 v } n is analyzed in the context of the smoothed-particle hydrodynamics (SPH) technique. The behaviour of these kernels for several values of the parameter n has been studied either analytically as well as numerically in connection with several tests carried out in two-dimensions. The main advantage of this kernel relies in its flexibility because for n = 3 it is similar to the standard widely used cubic-spline, whereas for n > 3 the interpolating function becomes more centrally condensed, being well suited to track discontinuities such as shock fronts and thermal waves.