TY - JOUR

T1 - Dustybox and dustywave: two test problems for numerical simulations of two-fluid astrophysical dust-gas mixtures

AU - Laibe, Guillaume

AU - Price, Daniel

PY - 2011

Y1 - 2011

N2 - In this paper we present the analytic solutions for two test problems involving two-fluid mix- tures of dust and gas in an astrophysical context. The solutions provide a means of bench- marking numerical codes designed to simulate the non-linear dynamics of dusty gas. The first problem, DUSTYBOX, consists of two interpenetrating homogeneous fluids moving with relative velocity difference. We provide exact solutions to the full non-linear problem for a range of drag formulations appropriate to astrophysical fluids (i.e., various prescriptions for Epstein and Stokes drag in different regimes). The second problem, DUSTYWAVE consists of the propagation of linear acoustic waves in a two-fluid gas-dust mixture. We provide the ana- lytic solution for the case when the two fluids are interacting via a linear drag term. Both test problems are simple to set up in any numerical code and can be run with periodic boundary conditions. The solutions we derive are completely general with respect to both the dust-to- gas ratio and the amplitude of the drag coefficient. A stability analysis of waves in a gas-dust system is also presented, showing that sound waves in an astrophysical dust-gas mixture are linearly stable

AB - In this paper we present the analytic solutions for two test problems involving two-fluid mix- tures of dust and gas in an astrophysical context. The solutions provide a means of bench- marking numerical codes designed to simulate the non-linear dynamics of dusty gas. The first problem, DUSTYBOX, consists of two interpenetrating homogeneous fluids moving with relative velocity difference. We provide exact solutions to the full non-linear problem for a range of drag formulations appropriate to astrophysical fluids (i.e., various prescriptions for Epstein and Stokes drag in different regimes). The second problem, DUSTYWAVE consists of the propagation of linear acoustic waves in a two-fluid gas-dust mixture. We provide the ana- lytic solution for the case when the two fluids are interacting via a linear drag term. Both test problems are simple to set up in any numerical code and can be run with periodic boundary conditions. The solutions we derive are completely general with respect to both the dust-to- gas ratio and the amplitude of the drag coefficient. A stability analysis of waves in a gas-dust system is also presented, showing that sound waves in an astrophysical dust-gas mixture are linearly stable

UR - http://users.monash.edu.au/~dprice/pubs/dust/index1.html

U2 - 10.1111/j.1365-2966.2011.19291.x

DO - 10.1111/j.1365-2966.2011.19291.x

M3 - Article

VL - 418

SP - 1491

EP - 1497

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 3

ER -