Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH

TL;DR

This paper examines how to better model discontinuities and Kelvin-Helmholtz instabilities in SPH simulations by proposing a new artificial thermal conductivity formulation that improves the treatment of contact discontinuities.

Contribution

It introduces a novel formulation of artificial thermal conductivity in SPH that reduces unnecessary dissipation and enhances the modeling of discontinuities and instabilities.

Findings

Improved handling of contact discontinuities in SPH.

Reduction of dissipation away from discontinuities.

Enhanced simulation of Kelvin-Helmholtz instabilities.

Abstract

In this paper we discuss the treatment of discontinuities in Smoothed Particle Hydrodynamics (SPH) simulations. In particular we discuss the difference between integral and differential representations of the fluid equations in an SPH context and how this relates to the formulation of dissip ative terms for the capture of shocks and other discontinuities. This has important implications for many problems, in particular related to recently highlighted problems in treating Kelvin-Helmholtz instabilities across entropy gradients in SPH. The specific problems pointed out by Agertz et al. (2007) are shown to be related in particular to the (lack of) treatment of contact discontinuities in standard SPH formulations which can be cured by the simple application of an artificial thermal conductivity term. We propose a new formulation of artificial thermal conductivity in SPH which minimises dissipation away from discontinuities and can therefore be applied quite generally in SPH calculations.