Dusty gas with SPH - I. Algorithm and test suite

TL;DR

This paper introduces a new SPH algorithm for simulating gas and dust mixtures, improving accuracy with double-hump kernels and validating it through a comprehensive test suite with known solutions.

Contribution

The paper presents a novel SPH algorithm for gas-dust mixtures, including a new kernel choice and a standardized test suite for validation.

Findings

Double-hump kernels significantly improve drag interpolation accuracy.

The spatial resolution criterion  < c_s t_s is essential for correct dynamics at high drag.

The algorithm successfully passes all benchmark tests with known solutions.

Abstract

We present a new algorithm for simulating two-fluid gas and dust mixtures in Smoothed Particle Hydrodynamics (SPH), systematically addressing a number of key issues including the generalised SPH density estimate in multi-fluid systems, the consistent treatment of variable smoothing length terms, finite particle size, time step stability, thermal coupling terms and the choice of kernel and smoothing length used in the drag operator. We find that using double-hump shaped kernels improves the accuracy of the drag interpolation by a factor of several hundred compared to the use of standard SPH bell-shaped kernels, at no additional computational expense. In order to benchmark our algorithm, we have developed a comprehensive suite of standardised, simple test problems for gas and dust mixtures: dustybox, dustywave, dustyshock, dustysedov and dustydisc, the first three of which have known analytic solutions. We present the validation of our algorithm against all of these tests. In doing so, we show that the spatial resolution criterion \Delta < cs ts is a necessary condition in all gas+dust codes that becomes critical at high drag (i.e. small stopping time ts) in order to correctly predict the dynamics. Implicit timestepping and the implementation of realistic astrophysical drag regimes are addressed in a companion paper.