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

TL;DR

This paper demonstrates that Smoothed Particle Hydrodynamics (SPH) methods inherently act as Lagrangian LES and are incompatible with eddy viscosity models due to implicit subfilter stresses, especially in turbulent flows.

Contribution

The study provides physical and numerical evidence that SPH methods cannot be effectively combined with eddy viscosity models for large eddy simulations of turbulence.

Findings

SPH acts as Lagrangian LES with overlapping elements causing implicit SFS.

Implicit SFS are significant in turbulent flow creation.

Eddy viscosity models degrade the turbulent transition process in SPH.

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.