Journal
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Volume 488, Issue 4, Pages 5290-5299Publisher
OXFORD UNIV PRESS
DOI: 10.1093/mnras/stz2035
Keywords
hydrodynamics; shock waves; methods: analytical; methods: numerical; protoplanetary discs
Categories
Funding
- Science and Technology Facilities Council
- Royal Society
- STFC [ST/P000592/1, 1949424] Funding Source: UKRI
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Motivated by the stability of dust laden vortices, in this paper we study the terminal velocity approximation equations for a gas coupled to a pressureless dust fluid and present a numerical solver for the equations embedded in the FARGO3D hydrodynamics code. We show that for protoplanetary discs it is possible to use the barycentre velocity in the viscous stress tensor, making it trivial to simulate viscous dusty protoplanetary discs with this model. We also show that the terminal velocity model breaks down around shocks, becoming incompatible with the two-fluid model it is derived from. Finally we produce a set of test cases for numerical schemes and demonstrate the performance of our code on these tests. Our implementation embedded in FARGO3D using an unconditionally stable explicit integrator is fast, and exhibits the desired second-order spatial convergence for smooth problems.
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