Simulating flow over and through porous media with application to erosion of particulate deposits

We simulate flows involving porous media and homogenous fluid using a single-domain finite-difference numerical method. The porous medium and unimpeded fluid are separated by a sharp interface where a stress jump boundary condition is implemented using a forcing term. The interface is constructed by connecting Lagrangian markers with cubic splines, allowing for any possible porous media geometry. This model is particularly flexible as it can easily account for a mobile interface. We apply our method to simulate erosion and suspension of particles from a fixed or erodible particulate deposit. The flux of particles entrained from the porous media is obtained from the computed velocity at the interface, in contrast to more common approaches that assume a flux proportional to the viscous stress at the interface.