E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh

By Volker Springel. 2009

1,596 citations recorded by the source corpus.

Hydrodynamic cosmological simulations at present usually employ either the Lagrangian smoothed particle hydrodynamics (SPH) technique or Eulerian hydrodynamics on a Cartesian mesh with (optional) adaptive mesh refinement (AMR). Both of these methods have disadvantages that negatively impact their accuracy in certain situations, for example the suppression of fluid instabilities in the case of SPH, and the lack of Galilean invariance and the presence of overmixing in the case of AMR. We here propose a novel scheme which largely eliminates these weaknesses. It is based on a moving unstructured mesh defined by the Voronoi tessellation of a set of discrete points. The mesh is used to solve the hyperbolic conservation laws of ideal hydrodynamics with a finite-volume approach, based on a second-order unsplit Godunov scheme with an exact Riemann solver. The mesh-generating points can in principle be moved arbitrarily. If they are chosen to be stationary, the scheme is equivalent to an ordinary Eulerian method with second-order accuracy. If they instead move with the velocity of the local flow, one obtains a Lagrangian formulation of continuum hydrodynamics that does not suffer from the mesh distortion limitations inherent in other mesh-based Lagrangian schemes. In this mode, our new method is fully Galilean invariant, unlike ordinary Eulerian codes, a property that is of significant importance for cosmological simulations where highly supersonic bulk flows are common. In addition, the new scheme can adjust its spatial resolution automatically and continuously, and hence inherits the principal advantage of SPH for simulations of cosmological structure growth. The high accuracy of Eulerian methods in the treatment of shocks is also retained, while the treatment of contact discontinuities improves. We discuss how this approach is implemented in our new code arepo, both in 2D and in 3D, and is parallelized for distributed memory computers. We also discuss techniques for adaptive refinement or de-refinement of the unstructured mesh. We introduce an individual time-step approach for finite-volume hydrodynamics, and present a high-accuracy treatment of self-gravity for the gas that allows the new method to be seamlessly combined with a high-resolution treatment of collisionless dark matter. We use a suite of test problems to examine the performance of the new code and argue that the hydrodynamic moving-mesh scheme proposed here provides an attractive and competitive alternative to current SPH and Eulerian techniques.

Subfields: Astronomy and Astrophysics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/d8f66f4093c21019bc15cffcb0130b9a0b1be04b

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Citations in the corpus

CO-dark gas and molecular filaments in Milky Way-type galaxies (2014, methodology): “These properties make AREPO an ideal tool for studying the formation of dense molecular gas in galactic spirals.”
A general model for the CO–H2 conversion factor in galaxies with applications to the star formation law (2011, methodology): “We note that recently the reliability of SPH for cosmological modelling has been called into question by comparisons between simulations done with GADGET-3 and others done with the new moving mesh code AREPO developed by Springel (2010).”
The illustris simulation: Public data release (2015, methodology): “The Illustris simulations employ the Arepo code (Springel, 2010) which evolves the equations of continuum hydrodynamics coupled with self-gravity.”
THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics (2012, result): “Similar differences were also observed in other works (see, e.g. Agertz et al. 2007; Springel 2010), and the presence (or absence) of these secondary instabilities has been often used as an indication of the numerical viscosity of the codes.”
AGN-driven quenching of star formation: morphological and dynamical implications for early-type galaxies (2013, result): “Another much more worrying aspect is the different behaviour of AMR and SPH codes as already underlined by Scannapieco et al. (2012) for Milky Way haloes, and then by Vogelsberger et al. (2012) who compared results from the AREPO code (moving mesh Springel 2010) with GADGET in a statistical sense.”
ON THE CLUSTER PHYSICS OF SUNYAEV–ZEL'DOVICH AND X-RAY SURVEYS. I. THE INFLUENCE OF FEEDBACK, NON-THERMAL PRESSURE, AND CLUSTER SHAPES ON Y–M SCALING RELATIONS (2011, methodology): “A recent comparison of a galaxy formation simulation with the SPH technique and the recently developed moving mesh code AREPO (Springel 2010) enabled – for the first time – to test the nature of the hydrodynamic solver with otherwise identical implementations of the gravity solver, the sub-resolutio”
Formation and evolution of primordial protostellar systems (2012, methodology): “AREPO is a finite-volume code that employs a Voronoi tessellation of space to compute hydrodynamic fluxes across cell boundaries (Springel 2010).”
Lyα COOLING EMISSION FROM GALAXY FORMATION (2010, methodology): “Work is underway to elucidate some of these hydrodynamical issues using the new shock-capturing, moving mesh code AREPO (Springel 2010).”
LIME - a flexible, non-LTE line excitation and radiation transfer method for millimeter and far-infrared wavelengths (2010, methodology): “This irregularity can be remedied by applied what is known as Lloyds algorithm (Lloyd 1982; Springel 2010), which iteratively moves a grid point slightly toward its Voronoi cells center of mass.”
Simulations of magnetic fields in isolated disc galaxies (2012, methodology): “Recently, we presented a first implementation of MHD in the Arepo code (Pakmor et al. 2011), which combines the accuracy of mesh-based techniques for hydrodynamics with the automatic adaptivity and geometric flexibility of particle based techniques such as SPH.”
Theoretical Challenges in Galaxy Formation (2016, methodology): “The newly developed moving mesh code AREPO (Springel 2010a) similarly suffers from numerical diffusion but combines advantages of the Lagrangian and Eulerian approaches and performs much better than traditional SPH codes like GADGET on mixing problems with a high convergence rate (Sijacki et al. 201”
HYDRODYNAMICAL SIMULATIONS TO DETERMINE THE FEEDING RATE OF BLACK HOLES BY THE TIDAL DISRUPTION OF STARS: THE IMPORTANCE OF THE IMPACT PARAMETER AND STELLAR STRUCTURE (2012, background): “The solution to the Riemann problem is sensitive to the velocity of the frame in which the problem is solved, and poor solutions can be returned in regions where the velocity of the frame is many times larger than the sound speed (Tasker et al. 2008; Robertson et al. 2010; Springel 2010).”
Introducing the Illustris Project: the evolution of galaxy populations across cosmic time (2014, methodology): “The Illustris simulations were evolved with the moving-mesh code AREPO (Springel 2010), which solves the Euler equations with Godunov’s scheme on a quasi-Lagrangian moving Voronoi mesh.”
The optical morphologies of galaxies in the IllustrisTNG simulation: a comparison to Pan-STARRS observations (2018, methodology): “Throughout this section, we express some distances in comoving coordinates (which is how distances are handled internally by MNRAS 000, 000–000 (0000) the AREPO code), which we indicate with a ‘c’ prefix.”
The cosmic merger rate of stellar black hole binaries from the Illustris simulation (2017, methodology): “The Illustris was run with the moving mesh code AREPO, to solve the inviscid Euler equations (Springel 2010).”
Stellar Feedback in Galaxies and the Origin of Galaxy-scale Winds (2011, background): “In particular, acceleration of cold gas directly by hot gas is difficult to treat accurately in SPH codes, and comparison with adaptive mesh schemes suggests that we are likely to underestimate the true amount of cold material in the wind (Springel 2010; Keres et al. 2011).”
ETHOS - an effective theory of structure formation: dark matter physics as a possible explanation of the small-scale CDM problems (2015, methodology): “Self-scattering of DM particles was implemented into the AREPO code (Springel 2010) following the probabilistic approach described in Vogelsberger et al. (2012), which assumes that scattering is elastic and isotropic.”