Shocking results without shocks: Subsonic turbulence in smoothed particle hydrodynamics and moving-mesh simulations

By Andreas Bauer, Volker Springel Hits, Zah. 2011

143 citations recorded by the source corpus.

Highly supersonic, compressible turbulence is thought to be of tantamount importance for star formation processes in the interstellar medium. Likewise, cosmic structure formation is expected to give rise to subsonic turbulence in the intergalactic medium, which may substantially modify the thermodynamic structure of gas in virialized dark matter halos and affect small-scale mixing processes in the gas. Numerical simulations have played a key role in characterizing the properties of astrophysical turbulence, but thus far systematic code comparisons have been restricted to the supersonic regime, leaving it unclear whether subsonic turbulence is faithfully represented by the numerical techniques commonly employed in astrophysics. Here we focus on comparing the accuracy of smoothed particle hydrodynamics (SPH) and our new moving-mesh technique AREPO in simulations of driven subsonic turbulence. To make contact with previous results, we also analyze simulations of transsonic and highly supersonic turbulence. We find that the widely employed standard formulation of SPH yields problematic results in the subsonic regime. Instead of building up a Kolmogorov-like turbulent cascade, large-scale eddies are quickly damped close to the driving scale and decay into small-scale velocity noise. Reduced viscosity settings improve the situation, but the shape of the dissipation range differs compared with expectations for a Kolmogorov cascade. In contrast, our moving-mesh technique does yield power-law scaling laws for the power spectra of velocity, vorticity and density, consistent with expectations for fully developed isotropic turbulence. We show that large errors in SPH's gradient estimate and the associated subsonic velocity noise are ultimately responsible for producing inaccurate results in the subsonic regime. In contrast, SPH's performance is much better for supersonic turbulence. [Abridged]

Subfields: Astronomy and Astrophysics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/72d7b82c4b8a548bbf0dedea1d4f192d33405c84

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Citations in the corpus

How supernova feedback turns dark matter cusps into cores (2011, background): “Mesh-based codes (Teyssier 2002; O’Shea et al. 2004; Springel 2010) highlight potential shortcomings of traditional SPH such as its poor handling of instabilities related to sharp density contrasts (Agertz et al. 2007; Bauer & Springel 2011).”
Star formation in galaxy mergers with realistic models of stellar feedback and the interstellar medium (2012, background): “The discrepancies above are also minimized when the flows of interest are supersonic (as opposed to subsonic), which is very much the case here (Kitsionas et al. 2009; Price & Federrath 2010; Bauer & Springel 2012).”
A general class of Lagrangian smoothed particle hydrodynamics methods and implications for fluid mixing problems (2012, methodology): “The former (larger-scale deviations), being dominated by artificial viscosity, are only indirectly tied to resolution; considering higher-resolution runs we confirm the results in Bauer & Springel (2012) regarding the relatively slow convergence the high-k spectrum in SPH relative to grid codes.”
A new class of accurate, mesh-free hydrodynamic simulation methods (2014, methodology): “…in the literature to difficulties of SPH methods in dealing with these instabilities (see e.g. Morris 1996; Dilts 1999; Ritchie & Thomas 2001; Marri & White 2003; Okamoto et al. 2003; Agertz et al. 2007; Kitsionas et al. 2009; Price & Federrath 2010; Bauer & Springel 2012; Sijacki et al. 2012).”
Galaxies on FIRE (Feedback In Realistic Environments): stellar feedback explains cosmologically inefficient star formation (2013, methodology): “…the results of grid codes and older SPH methods (such as that in Springel & Hernquist 2002) for certain problems (especially sub-sonic fluid mixing instabilities; see Agertz et al. 2007; Kitsionas et al. 2009; Bauer & Springel 2012; Vogelsberger et al. 2012; Sijacki et al. 2012; Kereš et al. 2012).”
Gasoline2: a modern smoothed particle hydrodynamics code (2017, background): “Other common labels include ‘standard’ SPH (Springel 2010a) and ‘classic’ SPH (Read, Hayfield & Agertz 2010; Bauer & Springel 2012).”
FIRE-2 simulations: physics versus numerics in galaxy formation (2017, background): “…of multi-phase winds moving sub-sonically or trans-sonically through a pressure-supported medium – precisely the regime where the known SPH errors are most problematic (O’Shea et al. 2005; Agertz et al. 2007; Read et al. 2010; Bauer & Springel 2012; Sijacki et al. 2012; Torrey et al. 2012).”
The star formation main sequence and stellar mass assembly of galaxies in the Illustris simulation (2014, methodology): “…gas inflow rates are less applicable to the Illustris simulation than to semi-analytical models because in Illustris gas accretion is explicitly treated using an accurate hydrodynamics algorithm (e.g. Sijacki et al. 2012; Vogelsberger et al. 2012; Kereš et al. 2012; Bauer & Springel 2012).”
Moving mesh cosmology: the hydrodynamics of galaxy formation (2011, background): “Moreover, the unphysical dissipation of shocks and subsonic turbulence in GADGET, as shown by Bauer & Springel (2012) (see also section 4.2 of Paper I), leads to the heating of the halo outskirts rather than of the central regions.”
Toy models for galaxy formation versus simulations (2013, methodology): “…the important small-scale processes involved in galaxy evolution, AMR codes offer a distinct advantage over SPH codes, e.g., because SPH does not accurately model processes such as shocks and hydrodynamical instabilities (e.g. Agertz et al. 2007; Scannapieco et al. 2012; Bauer & Springel 2012).”
The Auriga Project: the properties and formation mechanisms of disc galaxies across cosmic time (2016, background): “…frame of their trajectory and naturally provide high resolution in dense regions, they have difficulty in resolving the effects of shocks, and viscosity and noise effects in low-density regions can lead to artificial numerical quenching of the cooling rate in large haloes (Bauer & Springel 2012).”
Chaotic cold accretion on to black holes (2013, result): “As shown by comparison studies (e.g. Agertz et al. 2007; Tasker et al. 2008; Mitchell et al. 2009; Bauer & Springel 2012) fluid instabilities, discontinuities, mixing and turbulence are poorly resolved or even suppressed by SPH techniques.”
CO-dark gas and molecular filaments in Milky Way-type galaxies (2014, methodology): “In addition, AREPO has been shown to perform much better than standard SPH for modelling highly multiphase flows (Sijacki et al. 2012) and subsonic turbulence (Bauer & Springel 2012).”
Moving mesh cosmology: numerical techniques and global statistics (2011, methodology): “For example, Bauer & Springel (2012) show that while SPH does not accurately describe subsonic turbulence, in the supersonic regime, when the flow energy is mainly kinetic, GADGET and AREPO give similar answers.”
Stellar and Quasar Feedback in Concert: Effects on AGN Accretion, Obscuration, and Outflows (2015, background): “Together these variations produce the range of numerical effects which span the major SPH-grid code differences often discussed in the literature (see references above and Price & Federrath 2010; Bauer & Springel 2012; Sijacki et al. 2012).”
An improved SPH scheme for cosmological simulations (2015, methodology): “We show that the disagreement between Bauer & Springel (2012) and Price (2012a) is largely caused by technical differences, to solve it we propose a solution based on the D20 binning kernel.”
Phantom: A Smoothed Particle Hydrodynamics and Magnetohydrodynamics Code for Astrophysics (2017, methodology): “Adaptations of this module have also been incorporated into other SPH codes (Bauer & Springel, 2012; Valdarnini, 2016).”
Submillimetre galaxies in a hierarchical universe: number counts, redshift distribution, and implications for the IMF (2012, background): “Beyond the core 5 Recently, some authors (Agertz et al. 2007; Springel 2010b; Bauer & Springel 2012; Sijacki et al. 2012) have noted several significant flaws inherent in the traditional formulation of SPH, including the artificial suppression of fluid instabilities, artificial damping of turbulent…”
Compaction and quenching of high-z galaxies in cosmological simulations: blue and red nuggets (2014, methodology): “AMR codes more accurately trace some of the high-resolution hydrodynamical processes involved in galaxy formation than SPH codes that use the traditional density formulation (e.g. Agertz et al. 2007; Scannapieco et al. 2012; Bauer & Springel 2012).”
Simulating galaxy formation with black hole driven thermal and kinetic feedback (2016, methodology): “We thus also aim to take recent improvements in the accuracy of the hydrodynamical modelling into account (Bauer & Springel 2012; Kereš et al. 2012; Sijacki et al. 2012; Vogelsberger et al. 2012; Pakmor et al. 2016).”