SPH modelling of water flow inside a porous medium using a Riemann based formulation

Abstract

International audienceSimulating granular flows has been a major concern for thepast decades, with various environmental applications such asavalanches, landslides and scour near fluvial, coastal and off-shore constructions. These phenomena involve a porous matrixundergoing large deformations and characterized by a complexbehaviour. Thanks to its ability to handle large deformationsof the medium, SPH appears as a particularly advantageousmethod to deal with these problems. Various SPH schemesalready exist to model the granular medium behaviour, suchas the ones developed by Feng et al. [1], Bui and Nguyen [2](elastoplastic approach) or Gha¨ıtanellis [3] (elasto-viscoplasticapproach). However, to the authors’ knowledge, none of thesepapers show in their results what the water flow looks like insidethe porous structure while it deforms. Consequently, the presentwork aims at presenting a model to simulate the deformationof a granular medium as well as its infiltration by water. Theporous structure is unsaturated and is considered as a continuousmedium. Infiltrated water flows according to Darcy’s or Darcy-Forchheimer’s laws. Two different sets of particles are used forthis purpose, one for the water phase and an other one forthe porous structure, as done by Shimizu et al [4]. Riemann-based schemes have never been used yet for such purpose,though it proved to give accurate results for both fluid [6]and solid mechanics [7]. As a consequence, a new approachis proposed here by applying Riemann-based formulations onboth fluid and solid media. For the moment, the proposedmodel is not yet finished developing and only simulations withundeformable porous matrix are available for the writing of thisabstract. Results with moving, deformable porous matrix will bepresented during the conference