Single fluid versus multifluid: comparison between single-fluid and multifluid dust models for disc–planet interactions

Abstract

ABSTRACT Recent observations of substructures such as dust gaps and dust rings in protoplanetary discs have highlighted the importance of including dust into purely gaseous disc models. At the same time, computational difficulties arise with the standard models of simulating the dust and gas separately. These include the cost of accurately simulating the interactions between well-coupled dust and gas and issues of dust concentration in areas below resolution of the gas phase. We test a single-fluid approach that incorporates the terminal velocity approximation valid for small particles, which can overcome these difficulties, through modification of FARGO3D. We compare this single-fluid model with a multifluid model for a variety of planet masses. We find differences in the dust density distribution in all cases. For high-mass, gap-opening planets, we find differences in the amplitude of the resulting dust rings, which we attribute to the failure of the terminal velocity approximation around shocks. For low-mass planets, both models agree everywhere except in the corotation region, where the terminal velocity approximation shows overdense dust lobes. We tentatively interpret these as dusty equivalents of thermal lobes seen in non-isothermal simulations with thermal diffusion, but more work is necessary to confirm this. At the same resolution, the computational time for the terminal velocity approximation model is significantly less than a two-fluid model. We conclude that the terminal velocity approximation is a valuable tool for modelling a protoplanetary disc, but care should be taken when shocks are involved.