# Small dust grain dynamics on adaptive mesh-refinement grids. I. Methods

## TL;DR

This paper introduces a novel Eulerian numerical method for simulating small dust grain dynamics in star and disk formation, implemented in the RAMSES code, and demonstrates its accuracy and application to protostellar collapse scenarios.

## Contribution

It presents a new finite volume, second-order Godunov method for dust-gas mixtures with multiple dust species in adaptive mesh refinement codes.

## Key findings

- The scheme is second-order accurate on uniform grids.
- Dust grains larger than ~100 micrometers decouple from gas during collapse.
- The method successfully passes various benchmark tests.

## Abstract

Small dust grains are essential ingredients of star, disk and planet formation. We present an Eulerian numerical approach to study small dust grains dynamics in the context of star and protoplanetary disk formation. It is designed for finite volume codes. We use it to investigate dust dynamics during the protostellar collapse. We present a method to solve the monofluid equations of gas and dust mixtures with several dust species in the diffusion approximation implemented in the adaptive-mesh-refinement code RAMSES. It uses a finite volume second-order Godunov method with a predictor-corrector MUSCL scheme to estimate the fluxes between the grid cells. We benchmark our method against six distinct tests, dustyadvect, dustydiffuse, dustyshock, dustywave, settling and dustycollapse. We show that the scheme is second-order accurate in space on uniform grids and intermediate between second and first-order on non-uniform grids. We apply our method on various dustycollapse simulations of 1 solar mass cores composed of gas and dust. We developed an efficient approach to treat gas and dust dynamics in the diffusion regime on grid based codes. The canonical tests have been successfully passed. In the context of protostellar collapse, we show that dust is less coupled to the gas in the outer regions of the collapse where grains larger than approximately 100 micrometers fall significantly faster than the gas.