Modeling flow through a one-dimensional multi-layered soil profile using the Method of Lines

Abstract

The vertical flow of water through horizontal layers of soil is considered using the Method of Lines. Continuity of mass principles are used to develop the interface boundary conditions, by introducing fictitious points at the interface, and the boundary conditions are handled using explicit and iterative approximations. Both the pressure based, and the water content based forms of Richards' equation are solved using the Method of Lines. The solutions obtained are compared with some particular analytic solutions obtained from the literature, and the results show that good accuracy can be achieved. It is also shown that the water content model can handle a large discontinuity at the interface when compared against the analytical solution. This result is also confirmed against a numerical example from the literature, and was effective for relatively dry initial conditions.