Abstract
Abstract. 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.
Highlights
Water movement in soils is one of the key processes in the water cycle since it contributes to the renewal of groundwater resources through recharge, to vegetation growth through transpiration, to soil fertility through salinization/alteration and to atmospheric humidity through evaporation and transpiration
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
Because the pressure-based formulation does not ensure mass conservation – except for the approximation provided by Rathfelder and Abriola (1994) – and due to the limitations of the moisture-based formulation, the mixed formulation has been widely used since the work of Celia et al (1990)
Summary
Water movement in soils is one of the key processes in the water cycle since it contributes to the renewal of groundwater resources through recharge, to vegetation growth through transpiration, to soil fertility through salinization/alteration and to atmospheric humidity through evaporation and transpiration. An alternative algorithm has been suggested more recently where the parameters are kept unchanged within one time step and the time step is adapted to reach convergence This algorithm has been applied to the pressure-based form of RE by Kavetski and Binning (2002a) and to the soil moisture form by Crevoisier et al (2009), Ross (2003), and Zha et al (2013). This algorithm is called “non-iterative” because the parameters are not updated during the calculation, iterations may be necessary to adapt the magnitude of the time step. Ness of the algorithms applied to the mixed form of RE are evaluated using three different test cases
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