An investigation of temporal adaptive solution of Richards’ equation for sharp front problems

Accurate, reliable, efficient, and robust simulation of groundwater flow in the unsaturated zone for the problems that characterized by sharp fronts in both space and time is computationally expensive. The accurate numerical solution of these problems by standard approaches with uniform spatial and temporal discretization usually inefficient and simulation is too costly. Moreover, it is very difficult to obtain explicit solution of Richards' equation by using standard time integration unless very small time steps are used in the integration process. Economical and robust solution may be achieved with variable time step size instead of constant time step size use. In this study, adaptive method in time is used to solve Richards' equation with finite difference technique. Temporal adaptation is accomplished by using variable order, variable step size approximation. We show how a differential algebraic equation can give accurate solution, have good mass balance properties and more economical for a wide range solution accuracy. The accuracy and computational efficiency of the method are evaluated by comparison with a uniform spatial discretization that is adaptive in time for three problems simulating one-dimensional flow processes in unsaturated porous media. The results indicate that the method is quite competitive with spatially and temporally adaptive approach. We conclude that the method can be effectively implemented and efficient alternative to standard approaches for simulating variably saturated flow in one spatial dimension.