DUSTYBOX and DUSTYWAVE: two test problems for numerical simulations of twofluid astrophysical dustgas mixtures
Abstract
In this paper we present the analytic solutions for two test problems involving twofluid mixtures of dust and gas in an astrophysical context. The solutions provide a means of benchmarking numerical codes designed to simulate the nonlinear 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 nonlinear 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 twofluid gasdust mixture. We provide the analytic 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 dusttogas ratio and the amplitude of the drag coefficient. A stability analysis of waves in a gasdust system is also presented, showing that sound waves in an astrophysical dustgas mixture are linearly stable.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 December 2011
 DOI:
 10.1111/j.13652966.2011.19291.x
 arXiv:
 arXiv:1106.1736
 Bibcode:
 2011MNRAS.418.1491L
 Keywords:

 hydrodynamics;
 waves;
 methods: analytical;
 methods: numerical;
 dust;
 extinction;
 Astrophysics  Earth and Planetary Astrophysics;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 7 pages, 3 figures, MNRAS revised following minor referees comments. v2: Ancillary files for DUSTYWAVE solution attached