A NECESSARY CONDITION FOR INDIVIDUAL TIME STEPS IN SPH SIMULATIONS

By Takayuki R. Saitoh, J. Makino. 2008

146 citations recorded by the source corpus.

We show that the smoothed particle hydrodynamics (SPH) method, used with individual time steps in the way described in the literature, cannot handle strong explosion problems correctly. In the individual time-step scheme, particles determine their time steps essentially from a local Courant condition. Thus they cannot respond to a strong shock, if the pre-shock timescale is too long compared to the shock timescale. This problem is not severe in SPH simulations of galaxy formation with a temperature cutoff in the cooling function at 104 K, while it is very dangerous for simulations in which the multiphase nature of the interstellar medium under 104 K is taken into account. A solution for this problem is to introduce a time-step limiter which reduces the time step of a particle if it is too long compared to the time steps of its neighbor particles. Thus this kind of time-step constraint is essential for the correct treatment of explosions in high-resolution SPH simulations with individual time steps.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/923c004b12f53260dfea959f9c3528b4fdfe25ff

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Citations in the corpus

NIHAO project – I. Reproducing the inefficiency of galaxy formation across cosmic time with a large sample of cosmological hydrodynamical simulations (2015, background): “The Saitoh & Makino (2009) timestep limiter was implemented so that cool particles behave correctly when a hot blastwave hits them.”
FIRE-2 simulations: physics versus numerics in galaxy formation (2017, methodology): “Because we use adaptive timesteps, we also enforce a “wakeup” condition identical to that used for the hydrodynamics (see Saitoh & Makino 2009; Durier & Dalla Vecchia 2012); specifically, if an “active” particle in a sub-step interacts with an “inactive” particle in a timestep > 4 times larger…”
A new class of accurate, mesh-free hydrodynamic simulation methods (2014, methodology): “Similar catastrophic errors appear if one uses adaptive timesteps but removes the timestep limiter from Saitoh & Makino (2009); Durier & Dalla Vecchia (2012).”
Implementation of feedback in smoothed particle hydrodynamics: towards concordance of methods (2012, background): “…by guest on 28 July 2018 In a recent study of the modelling of SN feedback in smoothed particle hydrodynamics (SPH) simulations, Saitoh & Makino (2009) (hereafter SM09, see also Merlin et al. 2010) noted that strong perturbations of the internal energy of gas particles lead…”
Gasoline2: a modern smoothed particle hydrodynamics code (2017, methodology): “This test will break codes without careful time-step adjustment, as demonstrated in Saitoh & Makino (2009).”
Phantom: A Smoothed Particle Hydrodynamics and Magnetohydrodynamics Code for Astrophysics (2017, methodology): “This test is an excellent test for the individual timestepping algorithm, since it involves propagating a blast wave into an ambient medium of ‘inactive’ or ‘asleep’ particles, which can cause severe loss of energy conservation if they are not carefully awoken (Saitoh & Makino, 2009).”
A general class of Lagrangian smoothed particle hydrodynamics methods and implications for fluid mixing problems (2012, background): “However, as pointed out in Saitoh & Makino (2009) and developed further in Durier & Dalla Vecchia (2012), in problems with very high Mach number shocks/bulk flows, the standard adaptive timestepping can lead to problems if particles with long timesteps interact suddenly mid-timestep with material…”
The Dynamical and Chemical Evolution of Dwarf Spheroidal Galaxies with GEAR (2009, background): “This time step limiter is important when large differences in temperature occur between the pre- and post-shock media (Saitoh & Makino 2009; Merlin et al. 2010).”
The EAGLE simulations of galaxy formation: the importance of the hydrodynamics scheme (2015, background): “As was pointed out by Saitoh & Makino (2009), the conservation of energy in SPH following the injection of large amounts of energy requires the reduction of the integration time-step of the particles receiving energy as well as those of its direct neighbours.”
The physics of galactic winds driven by active galactic nuclei (2012, background): “…of a proper limiter neighboring smooth particle hydrodynamics particles that are initially at rest may not react adequately to sudden changes, which can lead to effects including inter-particle crossing and violation of energy conservation (Saitoh & Makino 2009; Durier & Dalla Vecchia 2012).”
Stellar and Quasar Feedback in Concert: Effects on AGN Accretion, Obscuration, and Outflows (2015, background): “…robust to these variations. improvements to the treatment of artificial viscosity (see Cullen & Dehnen 2010), SPH smoothing kernel accuracy (Dehnen & Aly 2012), and timestep communication relevant for treating extremely high Mach-number shocks (Saitoh & Makino 2009; Durier & Dalla Vecchia 2012).”
Galaxies on FIRE (Feedback In Realistic Environments): stellar feedback explains cosmologically inefficient star formation (2013, background): “As shown in Saitoh & Makino (2009) and Durier & Dalla Vecchia (2012), in problems with high Mach number flows, adaptive timesteps (without a limiter) can lead to errors if particles with long timesteps interact suddenly mid-timestep with those on much shorter timesteps.”
Smoothed Particle Hydrodynamics in Astrophysics (2010, methodology): “This problem can be avoided with an improved method for determining the sizes of individual timesteps (Saitoh & Makino, 2009).”
An improved SPH scheme for cosmological simulations (2015, methodology): “In our ‘new’ scheme, we use a particle wake-up time-step limiting scheme (see Saitoh & Makino 2009; Pakmor et al. 2012) as a solution, so as to shorten the time-steps whenever necessary and allow particles to become active earlier.”
NIHAO – IV: core creation and destruction in dark matter density profiles across cosmic time (2015, background): “ESF-GASOLINE2 also includes the time-step limiter suggested by Saitoh & Makino (2009), which is important in the presence of c© 2015 RAS, MNRAS000, 1–11 strong shocks and temperature jumps.”
A Superbubble Feedback Model for Galaxy Simulations (2014, background): “The extreme temperature jumps at strong shocks also require the time-step limiter of Saitoh & Makino (2009).”
Simulating galactic outflows with thermal supernova feedback (2012, methodology): “The new time-step is then propagated to the inactive neighbours following the scheme of Saitoh & Makino (2009).”