Analysis of intermittency in under-resolved smoothed-particle-hydrodynamics direct numerical simulations of forced compressible turbulence

Abstract

We perform three-dimensional under-resolved direct numerical simulations of forced compressible turbulence using the smoothed particle hydrodynamics (SPH) method and investigate the Lagrangian intermittency of the resulting hydrodynamic fields. The analysis presented here is motivated by the presence of typical stretched tails in the probability density function (PDF) of the particle accelerations previously observed in two-dimensional SPH simulations of uniform shear flow [Ellero et al., Phys. Rev. E 82, 046702 (2010)]. In order to produce a stationary isotropic compressible turbulent state, the real-space stochastic forcing method proposed by Kida and Orszag is applied, and the statistics of particle quantities are evaluated. We validate our scheme by checking the behavior of the energy spectrum in the supersonic case where the expected Burgers-like scaling is obtained. By discretizing the continuum equations along fluid particle trajectories, the SPH method allows us to extract Lagrangian statistics in a straightforward fashion without the need for extra tracer particles. In particular, Lagrangian PDF of the density, particle accelerations as well as their Lagrangian structure functions and local scaling exponents are analyzed. The results for low-order statistics of Lagrangian intermittency in compressible turbulence demonstrate the implicit subparticle-scale modeling of the SPH discretization scheme.