Abstract
To date, Lagrangian mass-transfer-based interacting particle methods have been shown to be rigorous and capable of modeling a diverse range of sophisticated problems but have lacked formal criteria for choosing an optimal time step length (\(\varDelta t\)). In Eulerian (grid-based) methods, a user can typically reduce \(\varDelta t\) to an arbitrary level and expect to see corresponding gains in accuracy. The particle methods that we consider behave similarly, but only up to a point: for a fixed number of particles, \(\varDelta t\) can become so small that the magnitude of diffusion restricts particles from communicating via mass-transfer, and at this point, solution accuracy begins to degrade. In this work, we formalize criteria for determining when this transition takes place, based on the properties of a particular system, and we use this criteria to choose the optimal \(\varDelta t\). We test these results with numerical experiments that demonstrate accurate prediction of the optimal \(\varDelta t\) for a variety of conditions.
Article Highlights
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We define the optimal time step length for mass-transfer particle tracking simulations.
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The guideline is shown to be effective for a variety of conditions.
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We provide guidance for determining the optimal time step for conditions different from those tested.
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Acknowledgements
We thank the editor and reviewers for their helpful and incisive comments. This work was supported by the US Army Research Office under Contract/Grant Number W911NF-18-1-0338, the US Department of Energy under award DE-SC0019123, and the National Science Foundation under award DMS-1911145. Sandia National Laboratories is a multi-mission laboratory managed and operated by the National Technology and Engineering Solutions of Sandia, L.L.C., a wholly owned subsidiary of Honeywell International, Inc., for the DOE’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.
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This work was supported by the US Army Research Office under Contract/Grant Number W911NF-18-1-0338, the US Department of Energy under award DE-SC0019123, National Science Foundation under award DMS-1911145, and by Sandia National Laboratories.
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The code used to generate the results in this manuscript is available at https://doi.org/10.5281/zenodo.5542405 (Schmidt et al. 2021).
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Schmidt, M.J., Engdahl, N.B., Benson, D.A. et al. Optimal Time Step Length for Lagrangian Interacting-Particle Simulations of Diffusive Mixing. Transp Porous Med 146, 413–433 (2023). https://doi.org/10.1007/s11242-021-01734-8
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DOI: https://doi.org/10.1007/s11242-021-01734-8