Hybrid finite volume-finite element model for the numerical analysis of furrow irrigation and fertigation

Authors: BRUNETTI, GIUSEPPE - UNIVERSITY OF CALIFORNIA; SIMUNEK, JIRKA - UNIVERSITY OF CALIFORNIA; Bautista, Eduardo

Submitted to: Computers and Electronics in Agriculture
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 5/8/2018
Publication Date: 5/12/2018
Citation: Brunetti, G., Simunek, J., Bautista, E. 2018. Hybrid finite volume-finite element model for the numerical analysis of furrow irrigation and fertigation. Computers and Electronics in Agriculture. 150,312-327. doi:https://doi.org/10.1016/j.compag.2018.05.013.
DOI: https://doi.org/10.1016/j.compag.2018.05.013

Interpretive Summary: A coupled surface-subsurface flow model was developed for modeling water and solute transport in furrow irrigation. The surface flow component solves a simplified form of the one-dimensional unsteady open channel flow equations, coupled to the advection dispersion equation, using finite volume techniques. The subsurface flow component solves the equation of partially saturated flow in porous media, coupled to the advection-dispersion equation for porous media. The well-known HYDRUS 2D/3D software package was used to model the subsurface flow. Accuracy of the finite volume solution for the surface flow was investigated as a function of the magnitude of the space and time steps used in the calculations. Results were also compared with predictions generated with the solute transport component of WinSRFR, developed by ARS, and with field measurements. Comparisons with WinSRFR are limited to surface flow concentrations and longitudinal distribution of the solute, as that model cannot predict the subsurface solute transport. Numerical performance of the model was satisfactory. Likewise, results compared favorably with predictions generated with WInSRFR and in comparison field measurements. Researchers interested in numerical procedures for solving coupled water and solute transport problems should find these results of interest.

Technical Abstract: Although slowly abandoned in developed countries, furrow irrigation systems continue to be a dominant irrigation method in developing countries. Numerical models represent powerful tools to assess irrigation and fertigation efficiency. While several models have been proposed in the past, the development of models that include a detailed description of solute transport in the furrow system and the root zone is desirable for both scientists and practitioners. This study presents a hybrid Finite Volume – Finite Element (FV-FE) model able to provide a mechanistic description of the coupled surface-subsurface processes occurring during furrow irrigation and fertigation. The numerical approach combines a one-dimensional description of water flow and solute transport in an open channel with a two-dimensional description of water flow and solute transport in a subsurface soil domain, thus reducing the dimensionality and complexity of the problem and the computational cost. A combination of advanced numerical techniques is used to increase the accuracy and reduce the computational cost. The modeling framework includes the widely used hydrological model, HYDRUS, which can simulate the movement of water, heat, and multiple solutes, as well as root water and nutrient uptake in variably-saturated porous media. First, the robustness of the proposed model is examined and confirmed by mesh and time step sensitivity analyses. Next, the model is theoretically and experimentally validated with satisfactory results against the well-established model WinSRFR and measured data from a furrow fertigation experiment in the US, respectively.