Air/Water Flow in Porous Media: A Comparison of Accurate and Efficient Numerical Methods

摘要

The research funded under this grant focused on solution algorithms for porous media flow models. We sought to improve both spatial and temporal computational methods for a range of problems associated with groundwater and surface water flows. Groundwater flow problems can be difficult to resolve for several reasons. The governing equations are nonlinear, as the permeability coefficient for the Darcy velocity depends on the saturation level. This dependence on saturation also means that the governing equation can change type, from parabolic to hyperbolic, or vice versa, as an infiltration front moves through the domain. In addition, the governing equation can change type as fluid flows from one material type to another (e.g., from sand to clay). In all cases, the challenges are both on the temporal and spatial domains.