Efficient methods for solving water flow in variably saturated soils under prescribed flux infiltration

Xiaoxian Zhang, A. Glyn Bengough, John W. Crawford, Iain M. Young

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


The non-linear solvers in numerical solutions of water flow in variably saturated soils are prone to convergence difficulties. Many aspects can give rise to such difficulties and in this paper we address the gravity term and the prescribed-flux boundary in the Picard iteration. The problem of the gravity term in the Picard iteration is iteration-to-iteration oscillation as the gravity term is treated, by analogy with the time-step advance technique, 'explicitly' in the iteration. The proposed method for the gravity term is an improvement of the 'implicit' approach of Zhang and Ewen [Water Resour. Res. 36 (2000) 2777] by extending it to heterogeneous soil and approximating the inter-nodal hydraulic conductivity in the diffusive term and the gravity term with the same scheme. The prescribed-flux boundary in traditional methods also gives rise to iteration-to-iteration oscillation because there is no feedback to the flux in the solution at the new iteration. To reduce such oscillation, a new method is proposed to provide such a feedback to the flux. Comparison with traditional Picard and Newton iteration methods for a wide range of problems show that a combination of these two proposed methods greatly improves the stability and consequently the computational efficiency, making the use of small time step and/or under-relaxation solely for convergence unnecessary. © 2002 Elsevier Science B.V. All rights reserved.
Original languageEnglish (US)
Pages (from-to)75-87
Number of pages13
JournalJournal of Hydrology
Issue number1-4
StatePublished - Mar 15 2002
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • Water Science and Technology


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