Open Access

ARTICLE

Exploring Capillary Fringe Flow: Quasilinear Modeling with Kirchhoff Transforms and Gardner Model

Rachid Karra^1,*, Abdelatif Maslouhi²

1 LASTIMI Laboratory, Mohammadia School of Engineers, Mohammed V University in Rabat, Rabat, Morocco
2 LIRNE Laboratory, Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco

* Corresponding Author: Rachid Karra. Email:

Fluid Dynamics & Materials Processing 2024, 20(7), 1611-1631. https://doi.org/10.32604/fdmp.2024.048447

Received 08 December 2023; Accepted 13 March 2024; Issue published 23 July 2024

Abstract

Recent studies have underscored the significance of the capillary fringe in hydrological and biochemical processes. Moreover, its role in shallow waters is expected to be considerable. Traditionally, the study of groundwater flow has centered on unsaturated-saturated zones, often overlooking the impact of the capillary fringe. In this study, we introduce a steady-state two-dimensional model that integrates the capillary fringe into a 2-D numerical solution. Our novel approach employs the potential form of the Richards equation, facilitating the determination of boundaries, pressures, and velocities across different ground surface zones. We utilized a two-dimensional Freefem++ finite element model to compute the stationary solution. The validation of the model was conducted using experimental data. We employed the OFAT (One_Factor-At-Time) method to identify the most sensitive soil parameters and understand how changes in these parameters may affect the behavior and water dynamics of the capillary fringe. The results emphasize the role of hydraulic conductivity as a key parameter influencing capillary fringe shape and dynamics. Velocity values within the capillary fringe suggest the prevalence of horizontal flow. By variation of the water table level and the incoming flow q, we have shown the correlation between water table elevation and the upper limit of the capillary fringe.

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Keywords

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