分野別セミナー

The most general integrable model for unsaturated one-dimensional groundwater infiltration governed by the Richards equation has been known since the 1980s. However, exact solutions for many simple, physically relevant boundary conditions have yet to be derived.
We present an exact series solution for infiltration subject to ponded water at the soil surface, by decomposing the soil body into saturated and unsaturated regions separated by a moving interface. The use of efficient, iterative, symbolic-computation algorithms removes restrictions on the number of terms that can be obtained in the final infiltration series. We are also able to consider behaviour in the popular but subtle nonlinear `delta-function diffusivity' limit within a wider class of exact solutions.