Understand
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.