rpSPH: a novel Smoothed Particle Hydrodynamics Algorithm

TL;DR

The paper introduces rpSPH, a new SPH discretisation that improves accuracy and reduces unphysical artifacts by evaluating pressure forces relative to local pressure, with minimal code changes.

Contribution

It proposes a novel pressure force evaluation method in SPH that enhances solution accuracy and stability compared to standard SPH.

Findings

Reduces particle noise and unphysical instabilities.

Improves accuracy in shock and instability simulations.

Requires fewer computational operations.

Abstract

We suggest a novel discretisation of the momentum equation for Smoothed Particle Hydrodynamics (SPH) and show that it significantly improves the accuracy of the obtained solutions. Our new formulation which we refer to as relative pressure SPH, rpSPH, evaluates the pressure force in respect to the local pressure. It respects Newtons first law of motion and applies forces to particles only when there is a net force acting upon them. This is in contrast to standard SPH which explicitly uses Newtons third law of motion continuously applying equal but opposite forces between particles. rpSPH does not show the unphysical particle noise, the clumping or banding instability, unphysical surface tension, and unphysical scattering of different mass particles found for standard SPH. At the same time it uses fewer computational operations. and only changes a single line in existing SPH codes. We demonstrate its performance on isobaric uniform density distributions, uniform density shearing flows, the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, the Sod shock tube, the Sedov-Taylor blast wave and a cosmological integration of the Santa Barbara galaxy cluster formation test. rpSPH is an improvement these cases. The improvements come at the cost of giving up exact momentum conservation of the scheme. Consequently one can also obtain unphysical solutions particularly at low resolutions.