Comments on "A mass-conservative switching algorithm for modeling fluid flow in variably saturated porous media, K. Sadegh Zadeh, Journal of Computational Physics, 230 (2011)"

Simulating coupled soil-aquifer systems are recently of great scientific interests and need, particularly in terms of getting a correct water exchange between regional climate and terrestrial surface/subsurface water body to predict the future changes in water resources for a sustainable agricultural production and drinking water coverage in areas with increasing aridification. The Richards equation has been widely used in simulating water flow processes in coupled soil-aquifer systems. It has been expressed in three standard forms: i) the pressure head-based form (h-based form) with pressure head as primary variable, ii) the saturation-based form with saturation as primary variable, and iii) the mixed form, in which either pressure or saturation can be chosen as primary variable [1,3,8]. Besides of the saturation-based form, the h-based and the mixed form which use the pressure head as the primary variable can be applied in the unsaturated zone and saturated zone simultaneously [2,6,8]. The mixed form is preferred by several researchers because it conserves mass more precisely [1,2,9], whereas the h-based form often leads to large mass-balance errors for highly non-linear problems such as infiltration into initially dry soil [1,2,9]. In the recent past Sadegh Zadeh [10] stated that the mixed form cannot be applied in the saturated zone: “. . . it is only applicable in unsaturated zones”. Based on this assumption, he proposed a switching algorithm which uses the mixed form of Richards equation in the unsaturated zone and switches to the h-based form in and near the saturated zone based on a threshold value of pressure head (−2.5 cm). The author concluded that this algorithm was designed to produce “rapid convergence for saturated and unsaturated regions for all types of initial and boundary conditions”.