An easy and efficient combination of the Mixed Finite Element Method and the Method of Lines for the resolution of Richards’ Equation

Abstract

In this work, the Mixed Hybrid Finite Element (MHFE) method is combined with the Method Of Lines (MOL) for an accurate resolution of the Richard's Equation (RE). The combination of these methods is often complicated since hybridization requires a discrete approximation of the time derivative whereas with the MOL, it should remain continuous. In this paper, we use the new mass lumping technique developed in Younes et al. [Younes, A., Ackerer, P., Lehmann, F., 2006. A new mass lumping scheme for the mixed hybrid finite element method. International Journal for Numerical Methods in Engineering 67, pp. 89–107.] for the MHFE method. With this formulation, the MOL is easily implemented and sophisticated time integration packages can be used without significant amount of work. Numerical simulations are performed on both homogeneous and heterogeneous porous media to show the efficiency and robustness of the developed scheme.