The purpose of this paper is to propose a time-step-robust cell-to-cell integration of particle trajectories in 3-D unstructured meshes in particle/mesh Lagrangian stochastic methods. The main idea is to dynamically update the mean fields used in the time integration by splitting, for each particle, the time step into sub-steps such that each of these sub-steps corresponds to particle cell residence times. This reduces the spatial discretization error. Given the stochastic nature of the models, a key aspect is to derive estimations of the residence times that do not anticipate the future of the Wiener process. To that effect, the new algorithm relies on a virtual particle, attached to each stochastic one, whose mean conditional behavior provides free-of-statistical-bias predictions of residence times. After consistency checks, this new algorithm is validated on two representative test cases: particle dispersion in a statistically uniform flow and particle dynamics in a non-uniform flow.

翻译：本文旨在提出一种针对粒子/网格拉格朗日随机方法中三维非结构化网格内粒子轨迹的单元间积分算法，该算法对时间步长具有鲁棒性。核心思想是通过为每个粒子将时间步长拆分为若干子步长（每个子步长对应粒子在单元内的驻留时间），从而动态更新时间积分中使用的平均场。这降低了空间离散误差。鉴于模型的随机特性，关键在于推导出不会预判维纳过程未来的驻留时间估计值。为此，新算法依赖于一个附着于每个随机粒子的虚拟粒子，其条件平均行为提供了无统计偏差的驻留时间预测。经过一致性检验后，该算法在两个代表性算例上得到验证：统计均匀流场中的粒子扩散与非均匀流场中的粒子动力学。