The standard approach to model variably saturated flow is using finite difference or finite element methods to solve Richards’ equation (RE). However, for highly non-linear problems, such as infiltration into very dry soils, these methods may suffer from mass-balance error, convergence problems and poor iterative efficiency.
Dr. WU mengxi, a senior engineer at the Key Laboratory of Environmental Mechanics, IMECH, CAS, provided a general, mass-conservative and computationally efficient multi-dimensional finite element algorithm. This algorithm has been integrated into the LinkFea software developed by him which has been used to solve underground flow problems in hydraulic engineering. In this study, a general numerical algorithm in the context of finite element scheme is developed, in which a mass-conservative, modified head based scheme (MHB) is proposed to approximate Richards’ equation, and mass-lumping techniques are used to keep the numerical simulation stable. The MHB scheme is compared with the modified Picard iteration scheme (MPI) in a ponding infiltration example. Although the MHB scheme is a little inferior to the MPI scheme in respect of mass balance, it is superior in convergence character and simplicity. The algorithm works well over a wide variety of problems, such as infiltration fronts, steady-state and transient water tables, and transient seepage faces, as demonstrated by its performance against published experimental data. The algorithm is presented in sufficient detail to facilitate its implementation.
The research entitled “A finite-element algorithm for modeling variably saturated flows” has been published in Journal of Hydrology, 2010, 394, 315-323.
Fig. Number of iterations required using (a) modified head based scheme or (b) modified Picard iteration.