A general-purpose timestep criterion for simulations with gravity

Abstract

We describe a new adaptive timestep criterion for integrating gravitational motion, which uses the tidal tensor to estimate the local dynamical timescale and scales the timestep proportionally. This provides a better candidate for a truly general-purpose gravitational timestep criterion than the usual prescription derived from the gravitational acceleration, which does not respect the equivalence principle, breaks down when $\mathbf{a}=0$, and does not obey the same dimensional scaling as the true timescale of orbital motion. We implement the tidal timestep criterion in the simulation code GIZMO, and examine controlled tests of collisionless galaxy and star cluster models, as well as fully-dynamic galaxy merger and cosmological dark matter simulations. The tidal criterion estimates the dynamical time faithfully, and generally provides a more efficient timestepping scheme compared to an acceleration criterion. Specifically, the tidal criterion achieves order-of-magnitude smaller energy errors for the same number of force evaluations in potentials with inner profiles shallower than $\rho \propto r^{-1}$ (ie. where $\mathbf{a}\to 0$), such as star clusters and cored galaxies. For a given problem these advantages must be weighed against the additional overhead of computing the tidal tensor on-the-fly, but in many cases this overhead is small.

Published in MNRAS

References in corpus (10)

• Athena: A New Code for Astrophysical MHD
• The Importance of Radiative Feedback for the Stellar Initial Mass Function
• N-body simulations of gravitational dynamics
• The origin of the Milky Way globular clusters
• The fine-grained phase-space structure of Cold Dark Matter halos
• Self-consistent proto-globular cluster formation in cosmological simulations of high-redshift galaxies
• Star cluster formation in cosmological simulations. III. Dynamical and chemical evolution
• DISCO: A 3D Moving-Mesh Magnetohydrodynamics Code Designed for the Study of Astrophysical Disks
• GANDALF - Graphical Astrophysics code for N-body Dynamics And Lagrangian Fluids
• An optimum time-stepping scheme for N-body simulations

Cited by in corpus (11)

• STARFORGE: Toward a comprehensive numerical model of star cluster formation and feedback
• Large-scale dark matter simulations
• The dynamics and outcome of star formation with jets, radiation, winds, and supernovae in concert
• Seeds Don't Sink: Even Massive Black Hole "Seeds" Cannot Migrate to Galaxy Centers Efficiently
• Can magnetized turbulence set the mass scale of stars?
• A New Discrete Dynamical Friction Estimator Based on $N$-body Simulations
• BIFROST: simulating compact subsystems in star clusters using a hierarchical fourth-order forward symplectic integrator code
• Fast Multipole Methods for $N$-body Simulations of Collisional Star Systems
• Novel Conservative Methods for Adaptive Force Softening in Collisionless and Multi-Species N-Body Simulations
• Accelerating self-gravitating hydrodynamics simulations with adaptive force updates
• Early Stages of Dusty Tori: The First Infrared Spectra from a Highly Multiscale Quasar Simulation