Dusty gas with one fluid
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In this paper, we show how the two-fluid equations describing the evolution of a dust and gas mixture can be re-formulated to describe a single fluid moving with the barycentric velocity of the mixture. This leads to evolution equations for the total density, momentum, the differential velocity between the dust and the gas phases and either the dust-to-gas ratio or the dust fraction. The equations are similar to the usual equations of gas dynamics, providing a convenient way to extend existing codes to simulate two-fluid mixtures without modifying the code architecture. Our approach avoids the inherent difficulties related to the standard approach where the two phases are separate and coupled via a drag term. In particular, the requirements of infinite spatial and temporal resolution as the stopping time tends to zero are no longer necessary. This means that both small and large grains can be straightforwardly treated with the same method, with no need for complicated implicit schemes. Since there is only one resolution scale the method also avoids the problem of unphysical trapping of one fluid (e.g. dust) below the resolution of the other. We also derive a simplified set of equations applicable to the case of strong drag/small grains, consisting of the standard fluid equations with a modified sound speed, plus an advection-diffusion equation for the dust-to-gas ratio. This provides a simple and fast way to evolve the mixture when the stopping time is smaller than the Courant time step. We present a smoothed particle hydrodynamics implementation in a companion paper.
Laibe , G & Price , D J 2014 , ' Dusty gas with one fluid ' Monthly Notices of the Royal Astronomical Society , vol. 440 , no. 3 , pp. 2136-2146 . DOI: 10.1093/mnras/stu355
Monthly Notices of the Royal Astronomical Society
© 2014 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society
DescriptionThis project was funded by the Australian Research Council (ARC) Discovery project grant DP1094585. DJP acknowledges funding via an ARC Future Fellowship, FT130100034.
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