A modified Picard iteration scheme for overcoming numerical difficulties of simulating infiltration into dry soil

• Published in: Journal of hydrology (Amsterdam) Vol. 551; pp. 56 - 69
• Main Authors: Zha, Yuanyuan, Yang, Jinzhong, Yin, Lihe, Zhang, Yonggen, Zeng, Wenzhi, Shi, Liangsheng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2017
• Subjects: Infiltration; Model robustness; Picard iteration; Richards’ equation; Variably saturated flow; Model robustness; Richards’ equation; Infiltration; Picard iteration; Variably saturated flow
• ISSN: 0022-1694; 1879-2707
• DOI: 10.1016/j.jhydrol.2017.05.053

•The reason of numerical divergence for simulating infiltration into dry soil is revealed.•The influencing factors of allowed maximum time step sizes are analyzed.•A more robust and cost-effective modified iteration algorithm is proposed. Numerical models based on Richards’ equation are often employed to simulate the soil water dynamics. Among them, those Picard iteration models which use the head as primary variable are widely adopted due to their simplicity and capability for handling partially saturated flow conditions. However, it is well-known that those models are prone to convergence failure in some unfavorable flow conditions, especially when simulating infiltration into initially dry soils. Here we analyze the reasons that give rise to the numerical difficulty. Moreover, several modifications to the mass-conservative Picard iteration method are proposed so that numerical difficulty is avoided in these unfavorable flow conditions. Our proposed modifications do not degrade the simulated results, while they lead to more robust convergence performances and cost-effective simulations.