Two fluid dust and gas mixtures in SPH: A semi-implicit approach

TL;DR

This paper introduces a semi-implicit SPH method for simulating dust-gas mixtures that reduces computational cost and dissipation, especially effective for small dust stopping times.

Contribution

It proposes a simple exponential decay model to efficiently approximate dust-gas drag forces in SPH simulations, avoiding explicit time integration.

Findings

Performs well across various tests with analytical comparisons

Provides significant speed-ups over explicit methods for small dust stopping times

Less dissipative than traditional explicit or implicit SPH approaches in dusty shock modeling

Abstract

A method to avoid the explicit time integration of small dust grains in the two fluid gas/dust smoothed particle hydrodynamics (SPH) approach is proposed. By assuming a very simple exponential decay model for the relative velocity between the gas and dust components, all the effective characteristics of the drag force can be reproduced. A series of tests has been performed to compare the accuracy of the method with analytical and explicit integration results. We find that the method performs well on a wide range of tests, and can provide large speed ups over explicit integration when the dust stopping time is small. We have also found that the method is much less dissipative than conventional explicit or implicit two-fluid SPH approaches when modelling dusty shocks.