Modélisation numérique d'un écoulement permanent dans un sol saturé

Abstract

This thesis focuses on the development of a two-dimensional numerical model to simulate steady-state flow in saturated porous media. The approach is initially based on the physical and hydrodynamic principles of hydrogeology, focusing on key parameters such as porosity, permeability, and hydraulic conductivity. The mathematical framework is established by combining Darcy's law and the mass conservation principle, resulting in the governing partial differential equation of the flow. Due to the complexity of analytical solutions, the Finite Difference Method (FDM) is implemented to discretize the spatial domain and convert the differential equations into an algebraic system. Finally, the developed model is used to map the hydraulic head distribution, calculate velocity fields, and perform a sensitivity analysis regarding the influence of the medium's hydraulic properties.