Modeling of unsaturated flow through porous media using meshless methods
Abstract
In this study, we focus on the modelling of infiltration process in porous media. We use the meshless techniques for efficiently solving the Richards equation which describes unsaturated water flow through soils. The design of approximate numerical methods for the Richards equation remains computationally challenging and requires the development of efficient numerical techniques. This difficulty is mainly due to the nonlinearity of the unsaturated hydraulic conductivity and the capillary pressure function. In this study, we develop a new method based on the localized radial basis function (RBF) and the Kirchhoff transformation technique in order to solve Richards equation in one and two-dimensional homogeneous medium. Our approach using the multiquadric radial basis function allows us to reduce the computational time and provide accurate numerical solutions. The proposed method does not require mesh generation. Picard's iterations are used to linearize the resulting nonlinear problem obtained using the Kirchhoff transformation technique. The numerical simulations show the capability of the proposed numerical techniques in predicting the dynamics of water through unsaturated soils.
Cite
@article{arxiv.2105.13133,
title = {Modeling of unsaturated flow through porous media using meshless methods},
author = {Mohamed Boujoudar and Abdelaziz Beljadid and Ahmed Taik},
journal= {arXiv preprint arXiv:2105.13133},
year = {2021}
}
Comments
The sandy clay and loam soils are selected in this numerical test to simulate unsaturated flow through a two-dimensional homogeneous medium. The time evolution of the total mass per unit of length of the 2D numerical solutions and the solutions simulated by 1D-Hydrus for a computational domain of unit length (1D problem) are displayed in Figure 2