N体模拟的一种新时间步长判据
A new timestep criterion for N-body simulations
AI总结：
推导了一种基于加速度、加加速度和snap的N体模拟新时间步长判据，能有效抵抗浮点舍入误差，在REBOUND的IAS15积分器中表现优于现有方法。
摘要：
我们推导了一个用于估计N体模拟中特征动力学时间尺度的新判据。该判据利用粒子位置的二阶、三阶和四阶导数：加速度、加加速度和snap。它可用于在具有自适应步长控制的积分器中选择时间步长。对于任何二体问题，无论偏心率如何，该判据都能保证确定轨道周期和近心点时间尺度。我们讨论了为什么我们的判据是具有上述特性的用于选择自适应时间步长的最简单的基于导数的表达式，并在数值测试中展示了其相对于现有判据的优越性能。由于我们的判据使用低阶导数，它不易受到由有限浮点精度引起的舍入误差的影响。这显著减少了自适应积分器由于非物理的时间步长估计而失败或卡住的相空间体积。例如，当使用双浮点精度时，我们的新判据可以准确估计位于距离坐标原点40AU处、大小为50m的太阳系天体周围轨道的时间步长。以前的方法仅限于大于10km的天体。我们在高阶IAS15积分器中实现了我们的新判据，该积分器是免费提供的N体软件包REBOUND的一部分。
英文摘要：
We derive a new criterion for estimating characteristic dynamical timescales in N-body simulations. The criterion uses the second, third, and fourth derivatives of particle positions: acceleration, jerk, and snap. It can be used for choosing timesteps in integrators with adaptive step size control. For any two-body problem the criterion is guaranteed to determine the orbital period and pericenter timescale regardless of eccentricity. We discuss why our criterion is the simplest derivative-based expression for choosing adaptive timesteps with the above properties and show its superior performance over existing criteria in numerical tests. Because our criterion uses lower order derivatives, it is less susceptible to rounding errors caused by finite floating point precision. This significantly decreases the volume of phase space where an adaptive integrator fails or gets stuck due to unphysical timestep estimates. For example, our new criterion can accurately estimate timesteps for orbits around a 50m sized Solar System object located at 40AU from the coordinate origin when using double floating point precision. Previous methods where limited to objects larger than 10km. We implement our new criterion in the high order IAS15 integrator which is part of the freely available N-body package REBOUND.
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