2021/05/19 by Mohamed Boujoudar, Boujoudar, Mohamed, Abdelaziz Beljadid +3
Engineering · #Dam Engineering and Safety #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Numerical Analysis (math.NA) #Numerical methods in engineering #Soil and Unsaturated Flow
paper · pdf · doi:10.48550/arxiv.2105.13133
openalex publication_date 2021/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.