Efficient Solution of the Coupled One-Dimensional Surface—Two-Dimensional Subsurface Flow during Furrow Irrigation Advance

Physically based modeling of the coupled one-dimensional surface and two-dimensional (2D) subsurface flow during furrow irrigation advance often causes numerical instabilities and nonconvergence problems. This is particularly the case for low irrigation advance rates when infiltration consumes a predominant part of the inflow volume. The proposed furrow advance phase model (FAPS) further develops the concepts of a previous study. An analytical zero-inertia surface flow model is iteratively coupled with the 2D subsurface water transport model HYDRUS-2. In contrast to the previous study, the flow domain is discretized using fixed space increments and the resulting set of nonlinear flow equations is solved using the Newton method. The complexity of the model was reduced by process adequate simplifications. FAPS exhibited better convergence, numerical stability, and less computational time than the original fixed time interval solution. The new solution converged rapidly for a number of model tests with various inflow rates including runs with very slow irrigation advance. Simulation model predictions agree very well with advance times measured in laboratory and field tests.