Bryan Quaife, Department of Scientific Computing, Florida State University
Transport in Viscous Eroded Media
Flow in porous media plays a crucial role in various geophysical, medical, and industrial applications. When the media undergoes mechanical erosion, preferred flow directions and anisotropic permeability develop. I will describe a high-order numerical method for solving the fluid equations and evolving the individual eroding grains. Using these eroded geometries, I will establish connections between the geometry's porosity and its associated tortuosity, dispersion, and anisotropy. In particular, I will show that eroded geometries permit flow in the longitudinal direction more easily than in the transverse direction by up to a factor of six. Finally, if time permits, I will present a new numerical method to simulate diffusion in complex eroded geometries. This method leverages the Laplace transform to determine long-time diffusion behaviors without applying conventional time stepping.