A semi-implicit finite element method for modeling fertilizer transport through soils with root water and nutrient uptake

Nour-Eddine Toutlini, Abdelaziz Beljadid and Azzeddine Soulaïmani

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 514-538

Abstract: Modeling the interactions of water flow, fertilizer, and root water and nutrient uptake in soils is crucial for optimizing water and nutrient management in agriculture. In this study, we propose a new semi-implicit finite element method for modeling fertilizer transport in unsaturated porous media. The numerical model incorporates root water and nutrient uptake by plants, considering passive, active, and combined passive–active uptake mechanisms. These processes add nonlinear terms that can lead to numerical issues which are addressed through the proposed semi-implicit treatments based on second-order Taylor approximation techniques. The proposed approach linearizes the system of governing partial differential equations in time. The effectiveness of the scheme is tested using numerical experiments. First, the coupled model of infiltration and solute transport in unsaturated zone connected to a groundwater table is simulated. Next, the transport of a urea–ammonium–nitrate fertilizer mixed with phosphorus and potassium fertilizers through the soil with subsurface drip fertigation is modeled where nitrogen transformations such as hydrolysis and nitrification are included. The performance of the proposed scheme is evaluated by comparing the results with those obtained using the well-established Hydrus software based on implicit methods. The numerical experiments demonstrate the robustness and accuracy of the proposed semi-implicit scheme in handling nonlinearities of the coupled system. These results demonstrate that the proposed approach offers an efficient alternative to standard implicit methods for modeling water and nutrient dynamics in unsaturated porous media.

Keywords: Fertilizers transport; Infiltration; Semi-implicit schemes; Root water and nutrient uptake; Finite element method (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475426001746
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:514-538

DOI: 10.1016/j.matcom.2026.04.032

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().