Numerical Modeling of Two‐Dimensional Transient Flow to Ditches

A numerical model of two‐dimensional transient saturated flow to ditches is presented. The model is based on a finite differences solution of the differential equation governing two‐dimensional transient flow in a heterogeneous and anisotropic porous medium. Thus, the model can account for the partial penetration of ditches, flow above the initial drain level, vertical anisotropy, vertical flows, and associated head losses. The model solutions are found to compare well with one‐dimensional Donnan and Kraijenhoff solutions when the relative resistance to vertical flow is negligible (i.e., $\mathrm{Kz}/\mathrm{Kx}\gg 1$). These analytical solutions are, however, found to underestimate the water‐table rise when $\mathrm{Kz}/\mathrm{Kx}<1\text{.}$ Design curves have been prepared for a few general cases of a partially penetrating ditch system.