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

Comparative Evaluation of Finite Difference and Finite Element Methods for Reactive Nitrogen Transport in Layered Sandy Loam with Wheat Root Uptake | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Comparative Evaluation of Finite Difference and Finite Element Methods for Reactive Nitrogen Transport in Layered Sandy Loam with Wheat Root Uptake Bello Abdulqadir, Yeak Su Hoe This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8137061/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract 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. Numerical Analysis Nitrogen transport Wheat root uptake Sandy loam soil Finite Difference Method (FDM) Finite Element Method (FEM) Soil heterogeneity Nutrient modeling Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Full Text Additional Declarations The authors declare potential competing interests as follows: TETFund Nigeria provided financial support for this research. The authors declare that they have no competing financial or non-financial interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8137061","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":558265355,"identity":"bc8fba98-d5cd-4258-b844-068234bdb0c7","order_by":0,"name":"Bello 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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\u0026ndash;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. 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