SPHS: Smoothed Particle Hydrodynamics with a higher order dissipation switch

TL;DR

This paper introduces SPHS, a higher order dissipation switch for Smoothed Particle Hydrodynamics that detects flow convergence early, improves mixing, ensures conservation, and allows multimass particles for better resolution control.

Contribution

The paper presents a novel second order accurate dissipation switch for SPH that enhances accuracy, mixing, and convergence, and enables multimass particle simulations.

Findings

Successfully resolves mixing issues in SPH

Achieves numerical convergence with increased resolution

Performs well on standard hydrodynamic tests

Abstract

We present a novel implementation of Smoothed Particle Hydrodynamics (SPHS) that uses the spatial derivative of the velocity divergence as a higher order dissipation switch. Our switch -- which is second order accurate -- detects flow convergence before it occurs. If particle trajectories are going to cross, we switch on the usual SPH artificial viscosity, as well as conservative dissipation in all advected fluid quantities (for example, the entropy). The viscosity and dissipation terms (that are numerical errors) are designed to ensure that all fluid quantities remain single-valued as particles approach one another, to respect conservation laws, and to vanish on a given physical scale as the resolution is increased. SPHS alleviates a number of known problems with `classic' SPH, successfully resolving mixing, and recovering numerical convergence with increasing resolution. An additional key advantage is that -- treating the particle mass similarly to the entropy -- we are able to use multimass particles, giving significantly improved control over the refinement strategy. We present a wide range of code tests including the Sod shock tube, Sedov-Taylor blast wave, Kelvin-Helmholtz Instability, the `blob test', and some convergence tests. Our method performs well on all tests, giving good agreement with analytic expectations.