Adaptive time-stepping for the Super-Droplet Method Monte Carlo collision-coalescence scheme
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911140886347776 |
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| author | Ware, Emma Bartman-Szwarc, Piotr Igel, Adele L. Arabas, Sylwester |
| author_facet | Ware, Emma Bartman-Szwarc, Piotr Igel, Adele L. Arabas, Sylwester |
| contents | We present an analysis of an adaptive time-stepping scheme for the Super-Droplet Method (SDM), a Monte Carlo algorithm for simulating particle coagulation. SDM represents cloud droplets as weighted superdroplets, enabling high-fidelity representations of microphysical processes such as collision-coalescence. However, the algorithm can undercount collisions when the expected number of events is not realizable given the superdroplet configuration, introducing a biased error referred here as the collision deficit. While SDM exhibits statistical spread inherent to Monte Carlo schemes, the deficit is a systematic underestimation of collision events. This error can be addressed with adaptive time-stepping, which dynamically adjusts simulation time steps to eliminate this deficit. We analyze the behavior of the deficit across a wide range of timesteps, superdroplet counts, and initialization strategies, and explore trade-offs between accuracy and efficiency. Using the classical Safranov-Golovin test case, we show that the deficit increases with timestep and superdroplet count, and that adaptive time-stepping effectively removes the associated error without significant cost. We test a smooth continuum of initial distributions with extrema representing two different initialization methods, and find that while the deficit is sensitive to the choice of attribute-space sampling strategies, adaptive time-stepping substantially reduces the difference, allowing for users to choose initialization methods optimized for other processes. We also propose a method of visualization, capturing both the attribute sampling, droplet interactions over multiple timesteps, and the deficit using network connectivity graphs. In 2-D flow-coupled simulations, we find the deficit can have a stronger effect on convergence than previously shown, with uncorrected deficit delaying the onset of precipitation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05536 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive time-stepping for the Super-Droplet Method Monte Carlo collision-coalescence scheme Ware, Emma Bartman-Szwarc, Piotr Igel, Adele L. Arabas, Sylwester Atmospheric and Oceanic Physics Computational Physics We present an analysis of an adaptive time-stepping scheme for the Super-Droplet Method (SDM), a Monte Carlo algorithm for simulating particle coagulation. SDM represents cloud droplets as weighted superdroplets, enabling high-fidelity representations of microphysical processes such as collision-coalescence. However, the algorithm can undercount collisions when the expected number of events is not realizable given the superdroplet configuration, introducing a biased error referred here as the collision deficit. While SDM exhibits statistical spread inherent to Monte Carlo schemes, the deficit is a systematic underestimation of collision events. This error can be addressed with adaptive time-stepping, which dynamically adjusts simulation time steps to eliminate this deficit. We analyze the behavior of the deficit across a wide range of timesteps, superdroplet counts, and initialization strategies, and explore trade-offs between accuracy and efficiency. Using the classical Safranov-Golovin test case, we show that the deficit increases with timestep and superdroplet count, and that adaptive time-stepping effectively removes the associated error without significant cost. We test a smooth continuum of initial distributions with extrema representing two different initialization methods, and find that while the deficit is sensitive to the choice of attribute-space sampling strategies, adaptive time-stepping substantially reduces the difference, allowing for users to choose initialization methods optimized for other processes. We also propose a method of visualization, capturing both the attribute sampling, droplet interactions over multiple timesteps, and the deficit using network connectivity graphs. In 2-D flow-coupled simulations, we find the deficit can have a stronger effect on convergence than previously shown, with uncorrected deficit delaying the onset of precipitation. |
| title | Adaptive time-stepping for the Super-Droplet Method Monte Carlo collision-coalescence scheme |
| topic | Atmospheric and Oceanic Physics Computational Physics |
| url | https://arxiv.org/abs/2509.05536 |