Numerical simulation of transient water infiltration in heterogeneous soils combining central schemes and mixed finite elements

Abstract

We present a new numerical scheme for the approximation of solutions of transient water infiltration problems in heterogeneous soils. The two-phase (water and air) flow problem is governed by a pressure-velocity equation coupled to a saturation equation. The numerical scheme combines a non-oscillatory, second-order, conservative central finite differencing scheme for the saturation equation with mixed finite elements for the pressure-velocity equation. An operator splitting technique allows for the use of distinct time steps for the solution of the equations of the governing system. One and two-dimensional numerical experiments show that the proposed scheme is able to capture accurately and efficiently sharp fronts in two-phase water-air problem. The simulations were carried out taking into account the effects of gravity and capillary diffusion forces.