Small dust grain dynamics on adaptive mesh refinement grids

Abstract

Context. Small dust grains are essential ingredients of star, disk and planet formation. Aims. We present an Eulerian numerical approach to study small dust grain 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. Methods. 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. Results. 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 firstorder on non-uniform grids. We apply our method on various dustycollapse simulations of 1M cores composed of gas and dust. Conclusions. We developed an efficient approach to treat gas and dust dynamics in the diffusion regime on grid-based codes. The canonical tests were 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 100 µm fall significantly faster than the gas.

Protostellar collapse: the conditions to form dust-rich protoplanetary disks

“…A gas and dust mixture with N small grains species can be modeled as a monofluid in the diffusion approximation (Laibe & Price 2014c;Price & Laibe 2015;Hutchison et al 2018;Lebreuilly et al 2019). This fluid, of density ρ, flows at its barycenter velocity v. The k-th dust phase, of density ρ k , has the specific velocity v + w k , where w k is the differential velocity between the dust and the barycenter.…”

“…For any quantity A, we defineĀ ≡ A/A 0 where A 0 is its initial value.¯ andθ are called the dust-ratio and dust-to-gas ratio enrichment respectively. Further details about the monofluid formalism and its implementation in RAMSES can be found in Lebreuilly et al (2019).…”

“…The RAMSES code is very proficient for problems that require a treatment of magnetohydrodynamics (Teyssier et al 2006;Masson et al 2012;Marchand et al 2018;Marchand et al 2019), radiation hydrodynamics Rosdahl et al 2013;Commerçon et al 2014;Rosdahl & Teyssier 2015;González et al 2015;Mignon-Risse et al 2020) or cosmic rays (Dubois & Commerçon 2016;Dubois et al 2019). We extended the code to the treatment of dust dynamics with multiple species in the diffusion approximation and terminal velocity regime (Lebreuilly et al 2019). The method, based on an operator splitting technique has been extensively presented and tested.…”

Numerical Methods for Simulating Star Formation

“…In recent years, Laibe and Price (2014a) proposed a monofluid formalism for the dust and gas mixture which is well adapted to regimes with St ≤ 1. This monofluid formalism has been implemented with success in SPH and grid-based codes in the past 5 years (Laibe and Price, 2014b;Lebreuilly et al, 2019). Last, Price and Laibe (2015), Lin and Youdin (2017) present methods for simulating the dynamics of small grains with only one additional equation on the dust concentration on top of the Euler equations.…”

“…Last, Price and Laibe (2015), Lin and Youdin (2017) present methods for simulating the dynamics of small grains with only one additional equation on the dust concentration on top of the Euler equations. These last methods have been recently implemented with success in PHANTOM , as well as in PLUTO (Chen and Lin, 2018) and in RAMSES (Lebreuilly et al, 2019).…”