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Abstract The ubiquity of microplastics in marine environments is of growing concern and is increasingly receiving widespread attention. Due to the role of rivers and streams as suppliers of microplastics to the marine environment, it is essential to accurately capture their movements at these scales, but modeling and experimental knowledge in such settings is still limited. In this work, three Markov models, including a continuous time random walk model, Bernoulli model, and spatial Markov model (SMM), are implemented to investigate polyethylene particles transport in open‐channel flows. First, a three‐dimensional high‐resolution direct numerical simulation (DNS) fully resolves a canonical open‐channel flow, and particle transport is simulated using idealized point particles. Then, a series of laboratory transport experiments are conducted in a circulating water tank, and particle image velocimetry methods are used to obtain particle‐tracking data. We find that the correlated Bernoulli model and SMM can successfully reproduce the transport of both DNS and laboratory experiments, particularly in the prediction of measured breakthrough curves, which highlights the importance of correlation between the successive steps. A major benefit of these models is a computational cost that is several orders of magnitude less than, for example, DNS, which demonstrates their high‐efficiency and effectiveness. Therefore, this research offers new insights into the transport of microplastics in open‐channel systems like rivers and streams, which is necessary to prevent and reduce the environmental hazards of microplastics. 

Abstract. Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work.For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.