Moving finite element model for one‐dimensional infiltration in unsaturated soil

Abstract

The numerical integration of Richards' equation for infiltration into homogeneous unsaturated soil is carried out by a moving finite element (MFE) method. Accurate solution of this one‐dimensional nonlinear partial differential equation by standard finite difference (FD) or finite element (FE) methods can be obtained by using a fine discretization on space and time. This can lead to large computer times. With the MFE method, grid points are moved during computation along the wetting front, so that accuracy can be maintained by using a small number of nodes for simulating cases several meters in depth. For these cases the MFE method is faster than FD and FE methods. The numerical MFE model is verified through comparison with the quasi‐analytical solution by Philip (1957). Moreover, we compare, for some other test problems, the computational efficiency of this method with that of two efficient pressure head‐based FD and FE fixed grid formulations.