Numerical modelling of interfacial soil erosion with viscous incompressible flows

The aim of this study is to develop a numerical model for simulating surface erosion occurring at a fluid/soil interface subject to a flow process. Balance equations with jump relations are used. A penalization procedure including a fictitious domain method is used to compute the Stokes flow around obstacles, in order to avoid body-fitted unstructured meshes and instead use fast and efficient finite volume approximations on Cartesian meshes. The evolution of the water/soil interface is described by using a level set function. The ability of the model to predict the interfacial erosion of soils is confirmed by several numerical simulations.