Two-dimensional interaction of a wetting front with an impervious layer: Analytical and numerical solutions

Wetting-front movement can be impaired whenever the flow region includes boundaries such as the soil surface, seepage faces, planes of symmetry, or actual layers that are effectively impermeable, such as heavy clays or coarse materials below the water-entry pressure. An approximate analytical solution for interaction of flow from a line source with a parallel plane, impervious layer is derived. The solution ignores gravity and assumes a particular diffusivity that is related to the constant flow rate. It is exact until interaction begins, and provides an accurate approximation for short times thereafter. It can therefore be used to test the accuracy of numerical solutions of the flow equation, which can then be used with confidence for later times when the analytical approximation breaks down, for instance because gravity is ignored. A finite difference solution was tested in this way for both gradual and steep wetting fronts. Agreement between the two solutions was excellent for the gradual front, with the analytical approximation only slightly in error at later times. Numerical errors at the steep front were much greater; an accurate solution needed a finer spatial grid and a restart from the exact analytical values at the beginning of the interaction. The analytical approximation, though not as accurate as for the gradual front, was still good.