Mathematical Modeling of Saturated‐Unsaturated Flow to Drains

Abstract

Two‐dimensional transient flow to ditches or drains in a heterogeneous, anisotropic porous medium is modeled for appropriate initial and boundary conditions using the finite differences method for the entire saturated‐unsaturated domain; numerically solving the governing ground water flow equation for the saturated zone below the water table; and using the Richards equation for the unsaturated zone. The water‐table rise computed by the composite flow model matches closely with observed water‐table rise in a tile‐drained experimental field. The composite flow model is superior to the saturated flow model (when based only on saturated flows), first, by accounting for the time of transfer of infiltration at the ground surface as recharge to the water table. Second, the general assumption of equal flux at the soil surface and at the water table is not required. The development of through flows has been studied in the presence of a clay layer in the unsaturated zone. Dependence of through flows on the thickness of clay layer and partial penetration has also been demonstrated. The model presented can also be used to calculate bank storage buildup during a flood and its subsequent release in a ditch or river having a ridge or a water divide parallel to the drain.