Simulation of unsaturated water flow around obstructions: three-dimensional Rankine bodies

Abstract

Sink and source combinations were used to simulate flow around barriers such as might exist within a stony, unsaturated soil system. Although more complicated than two-dimensional cases which were previously presented, the three-dimensional “Rankine bodies” are more appropriate for simulating flow around real objects. Generally, the appropriate potentials and velocity fields are easy to write down and evaluate, in fact, much easier than the alternative solutions based on scattering theory. Also, arrays of bodies can be arranged to simulate a repeated pattern rather than deal with only single barriers, cavities, etc. However, the shapes of the bodies are not known ahead of time and can only be roughly controlled. For the same Darcian flow, a simulated stony layer was shown to be wetter than that without stones and the effective saturated conductivity reduced somewhat less than 1 - f s where f s is the fraction of stones. Overall there is a qualitative agreement with previous theoretical and experimental results for both saturated and unsaturated flow.