© 2000, 2001, D. Baker & D. Scott

   Many of the current solutions to Richards' equation depend upon special mathematical forms of the diffusivity or conductivity, or are limited to special boundary conditions. This approach does not. It only requires that diffusivity and conductivity be expressible as continuous functions of relative saturation in a Fortran subroutine. It transforms Richards' equation from a second-order parabolic partial differential equation to a second-order elliptical boundary condition problem, solvable by the method of shooting. It is appropriate for non-hystertic unsaturated inflow into a 1-D homogeneous porous medium. Fortran programs for the exact solution and appropriate finite difference models used to confirm the results are available for download.

   This solution has a uniform grid in saturation, unlike the finite difference solutions used here which have a uniform grid in space. That means that the "exact" solution grid points with stick with the wetting front, no matter how sharp, at every time and depth. This makes it a viable independent solution for testing the effects of adaptive gridding schemes in finite difference solutions.

   These are draft versions of student tutorials. The first papers start with constant-head (constant water content) boundary condition cases in the horizontal and vertical. They refer in parts to some other tutorials on Green-Ampt infiltration that are not yet presented here. Additional drafts may be added for constant-inflow, variable-head and variable-inflow boundary conditions as the cases and software are worked out.