SDM Adaptive Timestepping
The original adaptive time-stepping scheme proposed herein extends the Super-Droplet Method (SDM) Monte Carlo algorithm. In SDM, each computational particle (super droplet) stands for a weighted ensemble of real droplets, allowing for detailed stochastic modelling of collisional coalescence and breakage. However, with a fixed timestep, the method can introduce a systematic bias which we refer to as the collision deficit, where too few collision events are realised compared to their statistical expectation.
The adaptive scheme dynamically adjusts the timestep to eliminate this deficit,
improving accuracy without compromising computational efficiency.
Validation in benchmark test cases shows that it reproduces the precision of short fixed timesteps while
retaining the speed of longer ones.
Implemented in the open-source PySDM Python package
(as well as in the Droplets.jl Julia package),
this approach enhances the reliability of probabilistic
coalescence modelling and provides a framework for more faithful representations of cloud microphysics.
Presentations and publications on the adaptive time-stepping for SDM
- Bartman 2020 (Atmospheric Physics Seminar talk, Univ. Warsaw, Poland): "PySDM: Pythonic particle-based cloud microphysics package"
- Bartman & Arabas 2023 (AMS Annual Meeting, Denver, CO, USA): "Adaptive Time-Stepping for Particle-Based Cloud Microphysics: Super-Droplet Transport, Collisions and Condensational Growth"
- Ware 2025 (Atmospheric Physics Seminar talk, Univ. Warsaw, Poland): "Adaptive Time-Stepping within the Super-Droplet Method Monte-Carlo Coagulation Scheme"
- Ware, Bartman-Szwarc et al. 2025 (arXiv e-print): "Adaptive time-stepping for the Super-Droplet Method Monte Carlo collision-coalescence scheme"
🎓 Student project opportunities
- Explore and document applicability of the adaptive scheme for drop breakup
Contributors from our team
Piotr Bartman-Szwarc
Emma Ware
