Physical Sciences and Mathematics Commons^™

A 3d Numerical Study Of Interface Effects Influencing Viscous Gravity Currents In A Parabolic Fissure, With Implications For Modeling With 1d Nonlinear Diffusion Equations, Eden Furtak-Cole, Aleksey S. Telyakovskiy

Mathematics and Statistics Student Research and Class Projects

Although one-dimensional non-linear diffusion equations are commonly used to model flow dynamics in aquifers and fissures, they disregard multiple effects of real-life flows. Similarity analysis may allow further analytical reduction of these equations, but it is often difficult to provide applicable initial and boundary conditions in practice, or know the magnitude of effects neglected by the 1D model. Furthermore, when multiple simplifying assumptions are made, the sources of discrepancy between modeled and observed data are difficult to identify. We derive one such model of viscous flow in a parabolic fissure from first principals. The parabolic fissure is formed by extruding …