Comparative Evaluation of Finite Difference and Finite Element Methods for Reactive Nitrogen Transport in Layered Sandy Loam with Wheat Root Uptake

Accurate simulation of nutrient transport in soil–plant systems is crucial for understanding nitrogen availability, uptake efficiency, and environmental losses. This study presents a comparative evaluation of the Finite Difference Method (FDM) and the Finite Element Method (FEM) in modeling nitrogen transport within sandy loam soil under wheat cultivation. Two representative problems were considered: (i) a one-dimensional vertical transport problem for benchmarking and (ii) a two-dimensional heterogeneous soil scenario with distributed wheat root sinks. Both methods incorporated Michaelis–Menten root uptake kinetics, heterogeneous diffusion coefficients, and a decaying flux boundary at the soil surface. The 1D problem demonstrated that both FDM and FEM reproduced the expected downward migration of nitrogen fronts and uptake-driven depletion zones. However, FEM provided smoother concentration fields and superior mass conservation, while FDM showed oscillatory residuals and sensitivity to discretization. In the 2D problem, FEM successfully captured spatial heterogeneity and root-induced depletion zones with minimal mass imbalance, whereas FDM underestimated depletion near deeper roots and exhibited cumulative mass loss. Overall, the results confirm that FEM is more robust for predictive simulations involving heterogeneity and root uptake, while FDM remains useful for exploratory studies due to its computational simplicity. These findings have direct implications for precision nitrogen management and sustainable agricultural practices in sandy loam systems.