LRBF meshless methods for predicting soil moisture distribution in root zone

• Main Authors: Boujoudar, Mohamed, Beljadid, Abdelaziz, Taik, Ahmed
• Format: Journal Article
• Language: English
• Published: 18-04-2024
• Subjects: Computer Science - Numerical Analysis; Mathematics - Analysis of PDEs; Mathematics - Numerical Analysis
• DOI: 10.48550/arxiv.2404.12453

In this paper, we first propose a coupled numerical model of unsaturated flow
in soils and plant root water uptake. The Richards equation and different
formulations are used in the developed numerical model to describe infiltration
in root zone and to investigate the impact of the plant root on the
distribution of soil moisture. The Kirchhoff transformed Richards equation is
used and the Gardner model is considered for capillary pressure. In our
approach, we employ a meshless method based on localized radial basis functions
(LRBF) to solve the resulting system of equations. The LRBF approach is an
accurate and computationally efficient method that does not require mesh
generation and is flexible in addressing high-dimensional problems with complex
geometries. Furthermore, this method leads to a sparse matrix system, which
avoids ill-conditioning issues. We implement the coupled numerical model of
infiltration and plant root water uptake for one, two, and three-dimensional
soils. Numerical experiments are performed using nontrivial analytical
solutions and available experimental data to validate the coupled numerical
model. The numerical results demonstrate the performance and ability of the
proposed numerical method to predict soil moisture dynamics in root zone.