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

Balvet Guilhem (), Minier Jean-Pierre (), Henry Christophe (), Roustan Yelva () and Ferrand Martin ()
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Balvet Guilhem: EDF R&D, 6 Quai Watier, 78400 Chatou, France; and CEREA, École des Ponts, EDF R&D, Île-de-France, France
Minier Jean-Pierre: EDF R&D, 6 Quai Watier, 78400 Chatou, France; and CEREA, École des Ponts, EDF R&D, Île-de-France, France
Henry Christophe: Université Côte d’Azur, Inria, CNRS, Sophia-Antipolis, France
Roustan Yelva: CEREA, École des Ponts, Champs-sur-Marne; and EDF R&D, Île-de-France, France
Ferrand Martin: EDF R&D, 6 Quai Watier, 78400 Chatou, France; and CEREA, École des Ponts, EDF R&D, Île-de-France, France

Monte Carlo Methods and Applications, 2023, vol. 29, issue 2, 95-126

Abstract: 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.

Keywords: Lagrangian stochastic modeling; particle-mesh PDF; temporal integration; trajectory in 3-D unstructured mesh; time-splitting methods; anticipation error (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1515/mcma-2023-2002

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