Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2009-09-02
Mon.Not.Roy.Astron.Soc.401:2463-2476,2010
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
Version accepted by MNRAS Oct 2, 2009. Figures degraded. For high-resolution color figures and movies of the numerical simulat
Scientific paper
10.1111/j.1365-2966.2009.15823.x
Eulerian hydrodynamical simulations are a powerful and popular tool for modeling 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.
Abel Tom
Gnedin Nickolay Y.
Kravtsov Andrey V.
Robertson Brant E.
Rudd Douglas H.
No associations
LandOfFree
Computational Eulerian Hydrodynamics and Galilean Invariance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Computational Eulerian Hydrodynamics and Galilean Invariance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computational Eulerian Hydrodynamics and Galilean Invariance will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-663207