A mass-conservative switching method for simulating saturated-unsaturated flow

Numerical solutions of water flow in variably saturated porous media may result in poor mass balance attributable to inherent nonlinear characteristics of the governing equation to describe the flow problem. In this study, a switching method was proposed for better mass balance in simulating saturated-unsaturated flow in soils with a large outflow boundary condition. The switching method is a combination of the h-based and mixed forms according to the local soil water condition. The h-based form is adopted if the absolute change of pressure heads between time steps is smaller than a threshold value (h0). Otherwise, the mixed form is applied. Based on simulations with various soils and initial conditions, a value of 3 cm is selected as the threshold value. The switching method extends applications of the mixed form to fully saturated soils by combining with the h-based form. The performance of the switching method was compared to that of the mixed form. The two methods were tested by simulating water flow in soils with different hydraulic characteristics. The switching method achieved convergence for all tested soils, whereas the mixed form failed to converge for 75% of the cases. Given the same tolerance level of numerical simulations, the switching method provided much better mass balance than the mixed form. For simulations on layered soils, the switching method again gave better mass balance than the mixed form. To achieve a similar mass balance level as the mixed formation, the switching method only needs large tolerance values for iterations, which makes the method efficient for long-time simulations of water flow in soils with frequent infiltration and deep drainage processes.