A study of energy spectra calculated with disordered particles

In this paper we study twomethods that have been used to calculate the kinetic energy spectra of a turbulent fluid when simulated by a particle method such as SPH. These are a direct particle summation DPS and a least squares LS method. These methods have been recently studied by Shi et al. who found that the LS method was superior. They calculated spectra derived from data at particle positions displaced from a regular grid according to a uniform probability distribution. Here we consider themore relevant case of particle positions from actual simulations of turbulence, and compare the results with those obtained by the random shifts from a regular grid. The results show that the LS method, while superior to the DPS method for particle positions produced by random shifts, is only comparable in accuracy to the DPS method when the positions are froman SPH turbulence simulation. Furthermore, the LSmethod requiresmore computation and its accuracy depends on a careful choice of a parameter. Both methods are accurate down to a resolution that is close to two particlespacings. Unlike Shi et al.we consider amuchwider range of energy spectra on which to base our conclusions.