Improving the convergence properties of the moving-mesh code AREPO

By Rüdiger Pakmor, Volker Springel, Andreas Bauer, Philip Mocz, D. Muñoz, Sebastian T. Ohlmann, Kevin Schaal, Chenchong Zhu. 2015

196 citations recorded by the source corpus.

Accurate numerical solutions of the equations of hydrodynamics play an ever more important role in many fields of astrophysics. In this work, we reinvestigate the accuracy of the moving-mesh code \textsc{Arepo} and show how its convergence order can be improved for general problems. In particular, we clarify that for certain problems \textsc{Arepo} only reaches first-order convergence for its original formulation. This can be rectified by simple modifications we propose to the time integration scheme and the spatial gradient estimates of the code, both improving the accuracy of the code. We demonstrate that the new implementation is indeed second-order accurate under the $L^1$ norm, and in particular substantially improves conservation of angular momentum. Interestingly, whereas these improvements can significantly change the results of smooth test problems, we also find that cosmological simulations of galaxy formation are unaffected, demonstrating that the numerical errors eliminated by the new formulation do not impact these simulations. In contrast, simulations of binary stars followed over a large number of orbital times are strongly affected, as here it is particularly crucial to avoid a long-term build up of errors in angular momentum conservation.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/f469a7ab51dd70971e794140368416448c344fec

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Citations in the corpus

FIRE-2 simulations: physics versus numerics in galaxy formation (2017, background): “…to calculate Sa; this is much more accurate and less noisy compared to common SPH or pure “face-based” mesh gradient estimators, which is important to reduce artificial numerical diffusivity (see e.g. Maron & Howes 2003; Luo et al. 2008; Lanson & Vila 2008; Mocz et al. 2014; Pakmor et al. 2016).”
Quenching and ram pressure stripping of simulated Milky Way satellite galaxies (2017, methodology): “The Auriga project consists of cosmological zoom-in simulations of ∼ 1012 M dark matter haloes within the ΛCDM paradigm conducted with the second-order accurate moving mesh code AREPO (Springel 2010; Pakmor et al. 2016).”
The Auriga Project: the properties and formation mechanisms of disc galaxies across cosmic time (2016, methodology): “The MHD equations are solved with a second-order Runge–Kutta integration scheme with high-accuracy least-squares spatial gradient estimators of primitive variables (Pakmor et al. 2016a) that improve on the estimators in the original version of AREPO (Springel 2010).”
Simulating galaxy formation with the IllustrisTNG model (2017, methodology): “For this reason, the Green-Gauss method has been replaced with a least-squares fit (LSF) method (Pakmor et al. 2016).”
The optical morphologies of galaxies in the IllustrisTNG simulation: a comparison to Pan-STARRS observations (2018, methodology): “…et al. 2018b; Springel et al. 2018) is a suite of magneto-hydrodynamic cosmological simulations run with the moving-mesh code AREPO (Springel 2010; Pakmor et al. 2011, 2016), featuring an updated version of the Illustris galaxy formation model (Vogelsberger et al. 2013; Torrey et al. 2014)…”
Gasoline2: a modern smoothed particle hydrodynamics code (2017, background): “AREPO suffered from some SPH-like numerical convergence issues, which have now been resolved (Mocz et al. 2015; Pakmor et al. 2016).”
First results from the IllustrisTNG simulations: the stellar mass content of groups and clusters of galaxies (2017, background): “These include an improved gradient estimate (Pakmor et al. 2016) that leads to better convergence properties of the hydrodynamics scheme as well as to an improved angular momentum conservation, a refined advection scheme for passive scalars used to track metals (Pillepich et al. 2018), and a…”
Simulating galaxy formation with black hole driven thermal and kinetic feedback (2016, methodology): “• An improved gradient estimator and time integration scheme for the hydrodynamics is used (Pakmor et al. 2016), which improves the accuracy of the AREPO code.”
First results from the IllustrisTNG simulations: matter and galaxy clustering (2017, background): “…have also been numerous technical advances in the underlying simulation code, such as improvements in the convergence rate of the hydrodynamical scheme (Pakmor et al. 2016) and the use of a more flexible hierarchical time integration for gravitational interactions (Springel et al. in preparation).”
Vertical disc heating in Milky Way-sized galaxies in a cosmological context (2015, methodology): “The mhd equations are solved with a second order Runge-Kutta integration scheme with high accuracy least square spatial gradient estimators of primitive variables (Pakmor et al. 2016), which are improvements to the original version of arepo (Springel 2010).”