Viscous Erosion of Porous Media

Fluid-mechanical erosion of solid materials occurs in many geological settings. One example is groundwater flow where the length and velocity scales are small, and the result is erosion of a porous media by a viscous fluid. Erosion creates channels of preferable flow direction and anisotropy, and standard groundwater flow models such as Darcy's Law are inappropriate. Therefore, we develop a numerical framework where individual grains are resolved. The method includes a fast-multipole-accelerated spectrally-accurate discretization of a boundary integral equation formulation, interface tracking that guarantees a uniform mesh for all time, and regularization terms that slight round-off sharp corners that erosion inevitably forms.