Numerical modeling of the flow in a completely saturated zone

Abstract

The flow through saturated porous soil is described by Darcy equation that generally has no analytical solution. Therefore, we have to use numerical methods to solve it. There exist several numerical methods and the well-known most used one is the finite elements method. In this work, we use a Diamond finite volumes scheme characterized with its conservation property to simulate Darcy equation in the linear and the non linear case in two dimensional case, based on permeability tensor. Different test cases are studied to validate the accuracy and the efficiency of the numerical model. The numerical scheme proves, through the obtained results, high level of accuracy comparing with the exact solution. The diamond finite volumes scheme for its ability to ensure the mass conservation of our model, knowing that the finite elements or the finite differences methods are less efficient on this side, our finite volumes method is the most suited to the Darcy flow and more faithful to physical problems comparing to other methods. We focused in our study on different aspects of the finite volumes scheme, the mass conservation, the non-linearity of the hydraulic conductivity and their interaction with the finite volumes method.

Keywords

• Finite volumes method
• Darcy equation
• Porous media