Modeling in nuclear waste isolation: Approximate solutions for flow in unsaturated porous media

Mathematical modeling plays a key role in the design and licensing of repositories for radioactive waste. Because safe isolation of nuclear waste involves extremely long time scales, and there exists very little engineering experience upon which to draw, modeling takes on a particularly crucial role. An example of a model problem motivated by hydrological issues in high-level waste isolation is presented. A repository concept involving storage in rock above the water table requires models for the flow of groundwater in unsaturated, porous media. Such flow is governed by an extremely nonlinear diffusion equation, and poses some difficult numerical challenges. A special form of the hydraulic conductivity function however, results in a linear field equation for steady-state problems, for which a boundary integral method yields very fast solutions