Unsaturated flow through a spherical inclusion

Abstract

Unsaturated flow is considered through a spherical inclusion. The hydraulic conductivity is of the form Kiexp(αh), where the saturated conductivity Ki is different in the main flow regime, the inclusion α is a constant in the entire flow domain, and h is the pressure head. The solution technique is analogous to that used by the authors previously to analyze flow through circular inclusions for two‐dimensional flow by reducing Richards' equation to the Helmholtz equation and applying the analytic element method. Comparisons show differences between the two‐dimensional case (circles) and three‐dimensional case (spheres) in terms of flow enhancement and exclusion through the inclusions. When the inclusion permeability is less than the background conductivity, a lesser fraction of flow occurs through the three‐dimensional case than for the two‐dimensional case; conversely, when the permeability is higher within the inclusion, there is a higher enhancement of flow through that region in the case of the three‐dimensional inclusion.