Smoothed Particle Hydrodynamics Physically Reconsidered -- The Relation to Explicit Large Eddy Simulation and the Issue of Particle Duality

In this work we will identify a novel relation between Smoothed Particle Hydrodynamics (SPH) and explicit Large Eddy Simulation (LES) using a coarse-graining method from Non-Equilibrium Molecular Dynamics (NEMD). 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 (SFS) modelling. We verify our theory by various simulations of homogeneous, isotropic turbulence (HIT) at $Re=10^4$ and compare the results to a Direct Numerical Simulation (DNS) reported by Dairay et al. (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 coarse-graining method for turbulent flows, highlighting its capabilities and limitations.
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