Time-step limiter

Enabled with command-line option --limiter.

The first limit we impose is to limit the time-step of active particles (section 3.4, Schaller et al. (2024), MNRAS 530:2). When a particle computes the size of its next time-step, typically using the CFL condition, it also additionally considers the time-step size of all the particles it interacted within the loop computing accelerations. We then demand that the particle of interest’s time-step size is not larger than a factor \(\Delta\) of the minimum of all the neighbours’ values. We typically use \(\Delta = 4\) which fits naturally within the binary structure of the time-steps in the code. This first mechanism is always activated in Swift and does not require any additional loops or tasks; it is, however, not sufficient to ensure energy conservation in all cases.

The time-step limiter proposed by Saitoh & Makino (2009) is also implemented in SWIFT and is a recommended option for all simulations not using a fixed time-step size for all particles. This extends the simple mechanism described above, by also considering inactive particles and waking them up if one of their active neighbours uses a much smaller time-step size.

This is implemented by means of an additional loop over the neighbours at the end of the regular sequence. Once an active particle has computed its time-step length for the next step, we perform an additional loop over its neighbours and activate any particles whose time-step length differs by more than a factor \(\Delta\) (usually also set to 4).

As shown by Saitoh & Makino (2009), this is necessary to conserve energy and hence yield the correct solution even in purely hydrodynamics problems such as a Sedov–Taylor blast wave. The additional loop over the neighbours is implemented by duplicating the already existing tasks and changing the content of the particle interactions to activate the requested neighbours.