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 2v )}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.