We describe a new adaptive time-step criterion for integrating gravitational motion, which uses the tidal tensor to estimate the local dynamical time-scale and scales the time-step proportionally. This provides a better candidate for a truly general-purpose gravitational time-step criterion than the usual prescription derived from the gravitational acceleration, which does not respect the equivalence principle, breaks down when a=0⁠, and does not obey the same dimensional scaling as the true time-scale of orbital motion. We implement the tidal time-step criterion in the simulation code GIZMO, and examine controlled tests of collisionless galaxy and star cluster models, as well as galaxy merger simulations. The tidal criterion estimates the dynamical time faithfully, and generally provides a more efficient time-stepping 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 ρ ∝ r⁻¹ (i.e. where a → 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.

中文翻译：

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重力模拟的通用时间步长标准

我们描述了一种用于整合引力运动的新的自适应时间步长标准，它使用潮汐张量来估计局部动态时间尺度并按比例缩放时间步长。这为真正通用的重力时间步长标准提供了比从重力加速度推导出的通常处方更好的候选者，它不遵守等效原理，在 a=0 时失效，并且不遵守相同的维度标度作为轨道运动的真实时间尺度。我们在模拟代码 GIZMO 中实现了潮汐时间步长标准，并检查了无碰撞星系和星团模型的受控测试，以及星系合并模拟。潮汐准则忠实地估计了动力时间，并且通常提供比加速度标准更有效的时间步进方案。具体来说，潮汐准则在内部剖面比 ρ ∝ r⁻¹（即其中 a → 0⁠）更浅的势能（例如星团和核星系）中，对于相同数量的力评估，实现了数量级较小的能量误差。对于给定的问题，必须权衡这些优势与动态计算潮汐张量的额外开销，但在许多情况下，这种开销很小。