3.17.4. Reflexive time steps

To make the particle evolution near-symplectic the most important aspect is that the time step determination should be reflexive, in the sense that when taking a timestep forward from t_A to t_B, the timestep should be evaluated in such a way that starting from t_B and moving backwards in time one should end up exactly at t_A. (Aiming for exact symplectic expressions would be overkill when there are weak and non-conservative perturbations from the moving gas).

A simple and efficient approximate method to achive this is to extrapolate the position forward one half (time index) step, using the previous positions, which are stored in the particle history. Details of the extrapolation may differ, e.g. in using or ignoring speed information – the main goal should be to obtain an estimate that is both cheap and accurate.