A Study of the Stability Properties of SPH

TL;DR

This paper investigates the stability issues in Smooth Particle Hydrodynamics (SPH), identifying causes of instability and proposing that higher order spline kernels can improve stability properties.

Contribution

It provides a detailed analysis of SPH instabilities and suggests that using higher order spline kernels enhances the method's stability.

Findings

SPH with momentum-conserving formulation is unstable to negative stress.

Lattice of SPH particles is unstable to transverse waves.

Higher order spline kernels improve SPH stability.

Abstract

When using a formulation of Smooth Particle Hydrodynamics (SPH) which conserves momentum exactly the motion of the particles is observed to be unstable to negative stress. It is also found that under normal circumstances a lattice of SPH particles is potentially unstable to transverse waves. This document is a summary of a detailed report (Morris 1994) investigating the nature of these and other instabilities in depth. Approaches which may be used to eliminate these instabilities are suggested. It is found that the stability properties of SPH in general improve as higher order spline interpolants, approximating a Gaussian, are used as kernels.