Fundamental differences between SPH and grid methods

Abstract

We have carried out a hydrodynamical code comparison study of 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 the SPH smoothing kernel over which information is not transferred.Comment: 15 pages, 13 figures, to be submitted to MNRAS. For high-resolution figures, please see http://www-theorie.physik.unizh.ch/~agertz

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“…Actually the point was rather more subtle, because "comparable resolution" depended on what quantity one was interested in. Thus, for example to obtain comparable power spectra in a volumeweighted quantity such as the kinetic energy required roughly equal numbers of SPH particles to Eulerian grid cells (and was thus about an order of magnitude more costly † Following the publication of Agertz et al (2007). The issue itself has nothing to do with Kelvin-Helmholtz instabilities but rather to the (non-)treatment of contact discontinuities in standard SPH schemes, in this case manifested when a KH instability problem is run across a contact discontinuity.…”