Diffusive Transport in Viscous Eroded Media

Flow in a fixed porous media is synonymous in many geophysical, medical, and industrial applications. However, when the geometry erodes, the porous media develops preferred flow directions and anisotropic permeability. By combining high-order numerical methods to solve the viscous fluid equations and to evolve individual grains, I will demonstrate how erosion can be simulated. Using these eroded geometries, I will draw connections between the porosity of the eroded geometry with tortuosity and dispersion. Finally, I will present a new numerical method to simulate diffusion in complex eroded geometries. This method uses the Laplace transform to find long time behaviors of diffusion without the need to perform time stepping.