Smoothed particle hydrodynamics physically reconsidered: The relation to explicit large eddy simulation and the issue of particle duality

Abstract

In this work, we will identify a novel relation between Smoothed Particle Hydrodynamics (SPH) and explicit large eddy simulation using a coarse-graining method from non-equilibrium molecular dynamics. While the current literature points at the conclusion that characteristic SPH issues become restrictive for subsonic turbulent flows, we see the potential to mitigate these SPH issues by explicit subfilter stress modeling. We verify our theory by various simulations of homogeneous, isotropic turbulence at =10$^4$ and compare the results to a direct numerical simulation [T. Dairay et al., “Numerical dissipation vs subgrid-scale modelling for large eddy simulation,” J. Comput. Phys. 337, 252–274 (2017)]. Although the simulations substantiate our theory, we see another issue arising, which is conceptually rooted in the particle itself, termed as particle duality. Finally, we conclude our work by acknowledging SPH as a coarse-graining method for turbulent flows, highlighting its capabilities and limitation