Evidence on the incompatibility of smoothed particle hydrodynamics and eddy viscosity models for large eddy simulations

Abstract

In this work, we will present evidence for the incompatibility of Smoothed Particle Hydrodynamics (SPH) methods and eddy viscosity models. Taking a coarse-graining perspective, we physically argue that SPH methods operate intrinsically as Lagrangian Large Eddy Simulations (LES) for turbulent flows with strongly overlapping discretization elements. However, these overlapping elements in combination with numerical errors cause a significant amount of implicit subfilter stresses (SFS). Considering a Taylor-Green flow at $Re=10^4$, the SFS will be shown to be relevant where turbulent fluctuations are created, explaining why turbulent flows are challenging even for current SPH methods. Although one might hope to mitigate the implicit SFS using eddy viscosity models, we show a degradation of the turbulent transition process, which is rooted in the non-locality of these methods.