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

Title
Efficient methods for solving water flow in variably saturated soils under prescribed flux infiltration
Publication Date
2002
Author(s)
Zhang, Xiaoxian
Bengough, A Glyn
Crawford, John W
Young, Iain
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Elsevier BV
Place of publication
Netherlands
DOI
10.1016/S0022-1694(01)00598-4
UNE publication id
une:5625
Abstract
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.
Link
Citation
Journal of Hydrology, v.260, p. 75-87
ISSN
0022-1694
Start page
75
End page
87

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