Numerical modeling of underground flow through porous media using volumes scheme

Abstract

The Richards equation attracts the attention of several researchers due to its importance in the hydrogeology field especially the flow through porous soil. It is a non linear partial differential equation that has no general analytic solution. Thus, the need to use numerical methods to solve it. In this work, a finite volumes scheme is used to simulate the pressure form and the mixed form of Richards equation in one dimension. Euler explicit and implicit schemes are used for the time discretization and a condition of scheme’s stability is given. Different test cases are done to validate the accuracy and the efficiency of the proposed numerical model