Fundamental differences between SPH and grid methods

TLDR

Grid and smoothed particle hydrodynamics (SPH) techniques differ markedly in their ability to model astrophysically important processes. The authors aim to explain that SPH’s standard implementation introduces spurious pressure forces at steep density gradients. This leads to a boundary gap roughly one smoothing kernel wide where particle interactions are severely damped. Their comparison of grid and SPH codes in modelling interacting multiphase fluids shows that Eulerian grid methods resolve dynamical instabilities such as Kelvin–Helmholtz and Rayleigh–Taylor, while SPH fails to capture these processes.

Abstract

We have carried out a comparison study of hydrodynamical codes by investigating their performance in modelling interacting multiphase fluids. The two commonly used techniques of grid and smoothed particle hydrodynamics (SPH) show striking differences in their ability to model processes that are fundamentally important across many areas of astrophysics. Whilst Eulerian grid based methods are able to resolve and treat important dynamical instabilities, such as Kelvin–Helmholtz or Rayleigh–Taylor, these processes are poorly or not at all resolved by existing SPH techniques. We show that the reason for this is that SPH, at least in its standard implementation, introduces spurious pressure forces on particles in regions where there are steep density gradients. This results in a boundary gap of the size of an SPH smoothing kernel radius over which interactions are severely damped.