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Computational Eulerian hydrodynamics and Galilean invariance

Robertson, Brant E. and Kravtsov, Andrey V. and Gnedin, Nickolay Y. and Abel, Tom and Rudd, Douglas H. (2010) Computational Eulerian hydrodynamics and Galilean invariance. Monthly Notices of the Royal Astronomical Society, 401 (4). pp. 2463-2476. ISSN 0035-8711.

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Eulerian hydrodynamical simulations are a powerful and popular tool for modelling fluids in astrophysical systems. In this work, we critically examine recent claims that these methods violate Galilean invariance of the Euler equations. We demonstrate that Eulerian hydrodynamics methods do converge to a Galilean-invariant solution, provided a well-defined convergent solution exists. Specifically, we show that numerical diffusion, resulting from diffusion-like terms in the discretized hydrodynamical equations solved by Eulerian methods, accounts for the effects previously identified as evidence for the Galilean non-invariance of these methods. These velocity-dependent diffusive terms lead to different results for different bulk velocities when the spatial resolution of the simulation is kept fixed, but their effect becomes negligible as the resolution of the simulation is increased to obtain a converged solution. In particular, we find that Kelvin–Helmholtz instabilities develop properly in realistic Eulerian calculations regardless of the bulk velocity provided the problem is simulated with sufficient resolution (a factor of 2–4 increase compared to the case without bulk flows for realistic velocities). Our results reiterate that high-resolution Eulerian methods can perform well and obtain a convergent solution, even in the presence of highly supersonic bulk flows.

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Additional Information:© 2009 The Authors. Journal compilation © 2009 RAS. Accepted 2009 October 2; received 2009 October 1; in original form 2009 September 2. BER would like to thank the staff of the Neonatal Intensive Care Unit at the Comer Childrens’ Hospital and the Mitchell Transitional Care Unit at the University of Chicago Medical Center for their hospitality while this work was completed. We also thank Anatoly Klypin, Brian O’Shea, Eve Ostriker, Volker Springel and Romain Teyssier for helpful discussions. BER gratefully acknowledges support from a Spitzer Fellowship through a NASA grant administrated by the Spitzer Science Center during the majority of this work. AVK is supported by the NSF under grants AST-0239759 and AST-0507666 and by NASA through grant NAG5-13274. BER and AVK were also partially supported by the Kavli Institute for Cosmological Physics at the University of Chicago. DHR gratefully acknowledges the support of the Institute for Advanced Study and the NSF through grant AST-0807444. Some of the simulations used in this work have been performed on the Joint Fermilab-KICP Supercomputing Cluster, supported by grants from Fermilab, Kavli Institute for Cosmological Physics and the University of Chicago.
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Kavli Institute for Cosmological PhysicsUNSPECIFIED
Institute for Advanced StudyUNSPECIFIED
Subject Keywords:hydrodynamics; instabilities; methods: numerical
Record Number:CaltechAUTHORS:20100216-100603480
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17484
Deposited By: Jason Perez
Deposited On:16 Feb 2010 19:04
Last Modified:25 Mar 2014 19:30

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