Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Random walk (RW) methods are recurring Monte Carlo methods used to modelconvective and diffusive transport in complex heterogeneous media. Many applications canbe found, including fluid mechanic, hydrology and chemical reactors modeling. These methodsare easy to implement, very versatile and flexible enough to become appealing for manyapplications because they generally overlook or deeply simplify the building of explicit complexmeshes required by deterministic methods. RWprovides a good physical understandingof the interactions between the space scales of heterogeneities and the transport phenomenaunder consideration. In addition, they can result in efficient upscaling methods, especiallyin the context of flow and transport in fractured media. In the present study, we review theapplications of RW to several situations that cope with diverse spatial scales and differentinsights into upscaling problems. The advantages and downsides of RW are also discussed,thus providing a few avenues for further works and applications.
ISSN: 0169-3913

insu-01308060
https://hal-insu.archives-ouvertes.fr/insu-01308060
DOI : 10.1007/s11242-016-0693-z

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We study diffusion in a heterogeneous medium that is characterized by spatially varying diffusion properties from a random walk point of view. We show that an inhomogeneous continuous time random walk (CTRW) with a spatially variable exponential transition time distribution solves the spatially discretized heterogeneous diffusion equation. This demonstrates the equivalence of the widely used time-domain random walk (TDRW) scheme and spatially inhomogeneous CTRW and at the same time provides a demonstration of the formal equivalence of the TDRW particle formulation and the heterogeneous diffusion equation. Based on this equivalence, we develop a TDRW method for heterogeneous diffusion under spatially variable multirate mass transfer properties. We discuss the implementation of these schemes and study the diffusion behavior in the presence of traps that are characterized by a truncated power-law trapping time distribution.
ISSN: 0309-1708

hal-00767566
https://hal.archives-ouvertes.fr/hal-00767566
DOI : 10.1016/j.advwatres.2012.07.015