Numerical modeling based on a finite element method for simulation of flow in furrow irrigation

In this study, a zero-inertia finite element model (ZIFEM) is developed and applied for simulating all phases of furrow irrigation based on Saint-Venant equations. The complexity and nonlinear behavior of the Saint-Venant equations are the major difficulty in developing a finite element model to simulate furrow irrigation. Therefore, through the Galerkin FEM approach, the model assesses the free surface flow on a variable cell length at each time step and determines the suitable element length for each individual cell and the model solves the equations by using an iterative method. Along with the free surface flow phase, the infiltration phase is estimated by the Kostiakov-Lewis equation. The ZIFEM model is verified using seven experimental data sets collected from the literature and observed data from the farm consisting of two free drainage furrows with a length of 72 m, a top width of 0.8 m, a depth of 0.25 m and a slope of 0.2%. The model accuracy is studied to simulate advance and recession trajectories and runoff by calculating the root-mean-square error (RMSE), relative error and percentage error. It is observed that in all irrigation events, the proposed model reasonably agreed with field measurements. An evaluation of the RMSE shows that in 81.25% irrigation events the ZIFEM is more accurate than the WinSRFR model. In overall, the results of the model suggest that the ZIFEM can be introduced as a potential numerical tool for analyzing and evaluating furrow irrigation.