FINITE-ELEMENT METHODS FOR MODELING WATER-FLOW IN VARIABLY SATURATED POROUS-MEDIA - NUMERICAL OSCILLATION AND MASS-DISTRIBUTED SCHEMES

The finite element method is an attractive numerical method for modeli ng water flow in variably saturated porous media due to its flexibilit y in dealing with complicated geometries. It is well known that the co nventional mass-distributed finite element method suffers from numeric al oscillations at the wetting front, especially for very dry initial conditions. Routinely, mass-lumped procedures are used to eliminate th em. This paper proposes a physical interpretation of the finite elemen t method applied to the water flow problem. With the finite element me thod, mass conservation is applied at the element level. The water sto rage and the flux within each element are split into several component s 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 tradi tional mass-distributed scheme can still generate an incorrect neighbo ring node response due to the highly nonlinear properties of water flo w in unsaturated soil and cause numerical oscillation. We propose two new mass-distributed schemes which are free of the numerical oscillati on, and reduce the smearing near the wetting front, at slightly increa sed CPU time.