A time-step-robust algorithm to compute particle trajectories in 3-D unstructured meshes for Lagrangian stochastic methods

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.

Automated summary

The purpose of this paper is to propose a time-step-robust cell-to-cell integration method for particle trajectories in 3D unstructured meshes. The main idea is to dynamically update mean fields used in time integration by splitting the time step into sub-steps corresponding to particle cell residence times. A virtual particle is introduced to estimate residence times without anticipating the future of the Wiener process. The algorithm is validated on two test cases: particle dispersion in a statistically uniform flow and particle dynamics in a non-uniform flow.