Accelerating self-gravitating hydrodynamics simulations with adaptive force updates

Many astrophysical hydrodynamics simulations must account for gravity, and evaluating the gravitational field at positions of all resolution elements can incur significant cost. Typical algorithms update position each element every time is updated hydrodynamically, but actual required frequencies gravity be different in general. We show that calculation optimised by only updating on a timescale dictated already-determined maximum timestep accurate integration $\Delta t_{\rm grav}$, while staying well within typical error budget hydro schemes solvers. Our implementation GIZMO code uses tidal introduced Grudi\'c & Hopkins 2020 to determine grav}$ force frequency turn, jerk evaluated solver construct predictor acceleration use between updates. test scheme standard self-gravitating problems, finding solutions very close na\"{i}ve far fewer forces, optimising simulations. also demonstrate $\sim 70\%$ speedup STARFORGE MHD GMC simulation, with larger gains likely higher-resolution runs. In general, this introduces new tunable parameter obtaining an optimal compromise accuracy computational cost, conjunction e.g. time-step tolerance, numerical resolution, tolerance.