DOI: 10.5194/hess-21-2667-2017
Scopus记录号: 2-s2.0-85020445816
论文题名: Ross scheme, Newton-Raphson iterative methods and time-stepping strategies for solving the mixed form of Richards' equation
作者: Hassane Maina F ; , Ackerer P
刊名: Hydrology and Earth System Sciences
ISSN: 10275606
出版年: 2017
卷: 21, 期: 6 起始页码: 2667
结束页码: 2683
语种: 英语
Scopus关键词: Adaptive algorithms
; Error analysis
; Heuristic algorithms
; Heuristic methods
; Newton-Raphson method
; Nonlinear equations
; Porous materials
; Solute transport
; Heuristic approach
; Iteration procedure
; Iterative algorithm
; Newton-Raphson iterative method
; Non-linear parameters
; Nonlinear properties
; Number of iterations
; Variably saturated
; Iterative methods
; algorithm
; error analysis
; flow modeling
; heuristics
; numerical model
; porous medium
; Richards equation
英文摘要: The solution of the mathematical model for flow in variably saturated porous media described by the Richards equation (RE) is subject to heavy numerical difficulties due to its highly nonlinear properties and remains very challenging. Two different algorithms are used in this work to solve the mixed form of RE: the traditional iterative algorithm and a time-adaptive algorithm consisting of changing the time-step magnitude within the iteration procedure while the nonlinear parameters are computed with the state variable at the previous time. The Ross method is an example of this type of scheme, and we show that it is equivalent to the Newton-Raphson method with a time-adaptive algorithm. Both algorithms are coupled to different time-stepping strategies: the standard heuristic approach based on the number of iterations and two strategies based on the time truncation error or on the change in water saturation. Three different test cases are used to evaluate the efficiency of these algorithms. The numerical results highlight the necessity of implementing an estimate of the time truncation errors. © Author(s) 2017. Citation statistics:
资源类型: 期刊论文
标识符: http://119.78.100.158/handle/2HF3EXSE/79163
Appears in Collections: 气候变化事实与影响
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作者单位: Laboratoire d'Hydrologie et de Géochimie de Strasbourg, Univ. Strasbourg/EOST - CNRS, 1 rue Blessig, Strasbourg, France; CEA-Laboratoire de Modélisation des Transferts dans l'Environnement, Bât. 225, Saint Paul lez Durance cedex, France
Recommended Citation:
Hassane Maina F,, Ackerer P. Ross scheme, Newton-Raphson iterative methods and time-stepping strategies for solving the mixed form of Richards' equation[J]. Hydrology and Earth System Sciences,2017-01-01,21(6)