Finite element methods for modeling water flow in variably saturated porous media: Numerical oscillation and mass‐distributed schemes

Abstract

The finite element method is an attractive numerical method for modeling water flow in variably saturated porous media due to its flexibility in dealing with complicated geometries. It is well known that the conventional mass‐distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Routinely, mass‐lumped procedures are used to eliminate them. This paper proposes a physical interpretation of the finite element method applied to the water flow problem. With the finite element method, mass conservation is applied at the element level. The water storage and the flux within each element are split into several components in the function space, each of which corresponds to one component of the boundary flux of the element. However, even though physical laws are correctly applied at the element level, it is shown that the traditional mass‐distributed scheme can still generate an incorrect neighboring node response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. We propose two new mass‐distributed schemes which are free of the numerical oscillation, and reduce the smearing near the wetting front, at slightly increased CPU time.