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Random walks with negative particles for discontinuous diffusion and porosity

Oukili, Hamza and Ababou, Rachid and Debenest, Gérald and Noetinger, Benoît Random walks with negative particles for discontinuous diffusion and porosity. (2019) Journal of Computational Physics, 396. 687-701. ISSN 0021-9991

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Official URL: https://doi.org/10.1016/j.jcp.2019.07.006


This study develops a new Lagrangian particle method for modeling flow and transport phenomena in complex porous media with discontinuities. For instance, diffusion processes can be modeled by Lagrangian Random Walk algorithms. However, discontinuities and heterogeneities are difficult to treat, particularly discontinuous diffusion or porosity. In the literature on particle Random Walks, previous methods used to handle this discontinuity problem can be characterized into two main classes as follows: “Interpolation techniques”, and “Partial reflection methods”. One of the main drawbacks of these methods is the small time step required in order to converge to the expected solution, particularly in the presence of many interfaces. These restrictions on the time step, lead to inefficient algorithms. The Random Walk Particle Tracking (RWPT) algorithm proposed here is, like others in the literature, discrete in time and continuous in space (gridless). We propose a novel approach to partial reflection schemes without restrictions on time step size. The new RWPT algorithm is based on an adaptive “Stop&Go” time-stepping, combined with partial reflection/refraction schemes, and extended with a new concept of negative mass particles. To test the new RWPT scheme, we develop analytical and semi-analytical solutions for diffusion in the presence of multiple interfaces (discontinuous multi-layered medium). The results show that the proposed Stop&Go RWPT scheme (with adaptive negative mass particles) fits extremely well the semi-analytical solutions, even for very high contrasts and in the neighborhood of interfaces. The scheme provides a correct diffusive solution in only a few macro-time steps, with a precision that does not depend on their size.

Item Type:Article
HAL Id:hal-02409018
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
French research institutions > IFP Energies Nouvelles - IFPEN (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Laboratory name:
Deposited On:19 Mar 2020 08:50

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