Two phase mixtures in SPH - A new approach

TL;DR

This paper introduces a novel one-fluid SPH method for simulating gas-dust mixtures that improves accuracy and efficiency by avoiding over-damping and dust trapping issues present in traditional two-fluid approaches.

Contribution

The authors develop a new single-fluid SPH formulation for gas-dust mixtures that conserves key quantities and simplifies to a diffusion model in the strong drag limit.

Findings

The method accurately models small grain/strong drag regimes.

It prevents dust particles from becoming trapped below gas resolution.

The approach is validated through tests and a preliminary protoplanetary disc application.

Abstract

We present a new approach to simulating mixtures of gas and dust in smoothed particle hydrodynamics (SPH). We show how the two-fluid equations can be rewritten to describe a single-fluid 'mixture' moving with the barycentric velocity, with each particle carrying a dust fraction. We show how this formulation can be implemented in SPH while preserving the conservation properties (i.e. conservation of mass of each phase, momentum and energy). We also show that the method solves two key issues with the two fluid approach: it avoids over-damping of the mixture when the drag is strong and prevents a problem with dust particles becoming trapped below the resolution of the gas. We also show how the general one-fluid formulation can be simplified in the limit of strong drag (i.e. small grains) to the usual SPH equations plus a diffusion equation for the evolution of the dust fraction that can be evolved explicitly and does not require any implicit timestepping. We present tests of the simplified formulation showing that it is accurate in the small grain/strong drag limit. We discuss some of the issues we have had to solve while developing this method and finally present a preliminary application to dust settling in protoplanetary discs.