Jonathan Bode, George Mason University


Homogenization Methods for Porous Media Flows

Abstract:  This project involves the study of fluid flows through porous media whose permeability may be a rapidly-varying function of space. The understanding of such fluid flows are important in emerging technologies for remediation of porous media systems contaminated by nonaqueous phase liquids. A homogenization procedure provides both a leading-order description and a means to identify explicit correction formulas that can be processed and compared with full numerical simulations. In this presentation we assess a new asymptotic correction formula for the porous media equation, a nonlinear partial differential equation describing the fluid motion of a gravity current in heterogeneous porous media, in an effort to obtain a uniformly-valid correction formula for the leading-order homogenized solution.


Undergraduate Mentor: Dan Anderson (GMU)