UC Merced

We simulate flows involving porous media and homogenous fluid using a single-domain finite-difference numerical method. We study numerically the settling of a porous sphere in a density-stratified ambient fluid. Simulations are validated against prior laboratory experiments and compared to two mathematical models. Two main effects cause the particle to slow down as it enters a density gradient: lighter fluid within the particle and entrainment of the density-stratified ambient fluid. The numerical simulations accurately capture the particle retention time. We quantify the delay in settling due to ambient fluid entrainment and lighter internal fluid becoming denser through diffusion as a function of the Reynolds, P eclet, and Darcy numbers, as well as the thickness of the transition layer and the ratio of the density difference between the lower and upper fluid layer to the density difference between the particle and the upper layer. A simple fitting formula is presented to describe the settling time delay as a function of each of those five non-dimensional parameters.

We introduce a new numerical method specially designed for fluid-porous simulations. 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 particulate deposit. The flux of particles separated from porous media ascribable to a moving fluid is obtained from the computed velocity across the interface, in contrast to more common approaches that assume a flux proportional to the viscous stress at the interface.