Modeling Flow Through a One-Dimensional Multi-Layered Soil Profile Using the Method of Lines

Matthews, Christopher John; Braddock, Roger David; Sander, G. C.

doi:10.1023/b:enmo.0000032092.10546.c6

Cited by 33 publications

(38 citation statements)

References 18 publications

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“…-TC2: infiltration in a homogeneous soil initially at hydrostatic equilibrium with a prescribed constant flux at the soil surface and prescribed pressure at the bottom (Miller et al, 1998); and -TC3: infiltration/evaporation in an initially dry heterogeneous soil, with variable positive and negative fluxes at the surface and free drainage at the base of the soil column (Lehmann and Ackerer, 1998).…”

Section: Evaluation Of the Algorithms' Performancementioning

confidence: 99%

“…This test case models an infiltration in a 200 cm vertical column of unconsolidated clay loam with non-uniform grain size distribution and was considered by Miller et al (1998) to be a very challenging test. This problem was found to be more challenging from the numerical point of view compared to TC1 due to the relative permeability function that enhances the nonlinear behavior of Richards' equation (Figs.…”

Section: Tc2: Infiltration In a Homogenous Soil With Hydrostatic Initmentioning

confidence: 99%

“…Alternative iterative methods are based on transform formulations (Crevoisier et al, 2009;Ross and Bristow, 1990;Williams et al, 2000;Zha et al, 2013) or the method of lines (Fahs et al, 2009;Matthews et al, 2004;Miller et al, 1998;Tocci et al, 1997).…”

Section: Introductionmentioning

confidence: 99%

“…The method of lines using the DASPK integrator was applied to the Richards' equation by Matthews et al (2004), Miller et al (1998), andTocci et al (1997), among others. The method of lines consists of discretization of the spatial part of the PDE only, leading to a system of ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…It has been found to be significantly more efficient than other temporal discretizations (Miller et al, 2006). However, Kavetski and Binning (2002b) reported difficulties in obtaining convergence for the DASPK solver associated with an arithmetic mean of inter-block conductivities for the most difficult problem addressed by Miller et al (1998). Additionally, very few non-iterative schemes have been developed Binning, 2004, 2002a;Paniconi et al, 1991).…”

Section: Introductionmentioning

confidence: 99%

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Ross scheme, Newton–Raphson iterative methods and time-stepping strategies for solving the mixed form of Richards' equation

Maina

Ackerer

2017

Hydrol. Earth Syst. Sci.

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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 timestep 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 NewtonRaphson 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.

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Section: Evaluation Of the Algorithms' Performancementioning

confidence: 99%

Section: Tc2: Infiltration In a Homogenous Soil With Hydrostatic Initmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Ross scheme, Newton–Raphson iterative methods and time-stepping strategies for solving the mixed form of Richards' equation

Maina

Ackerer

2017

Hydrol. Earth Syst. Sci.

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Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils

et al. 2019

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Modeling variably saturated flow in the vadose zone is of vital importance to many scientific fields and engineering applications. Richardson-Richards equation (RRE, which is conventionally known as Richards' equation) is often chosen to physically represent the fluxes in the vadose zone when the accurate characterization of the soil water dynamics is required. Being a highly nonlinear partial differential equation, RRE is often solved numerically. Although there are mature software and codes available for simulating variably saturated flow by solving RRE, the numerical solution of RRE is nevertheless computationally expensive.Moreover, sometimes the robustness and the efficiency of RRE-based models can deteriorate rapidly when certain unfavorable conditions are met. These demerits of RRE hinder its application on large-scale vadose zone hydrology problems and uncertainty quantification, both of which requires many runs of the prediction model. To address these challenges, the accuracy, convergence, and efficiency of the numerical schemes of RRE should be further improved by testing a wide variety of cases covering different initial conditions, boundary conditions, and soil types. We reviewed and highlighted several critical issues related to the numerical modeling of RRE, including spatial and temporal discretization, the different forms of RREs, iterative and noniterative schemes, benchmark solutions, and available software and codes. Based on the review, we summarize the challenges and future work for solving RRE numerically.

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Soil–water and solute movement under precision irrigation: knowledge gaps for managing sustainable root zones

et al. 2007

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1Precision irrigation involves the accurate and precise application of water to meet the 2 specific requirements of individual plants or management units and minimize adverse 3 environmental impact. Under precision irrigation applications, water and associated solute 4 movement will vary spatially within the root zone and excess water application will not 5 necessarily result in deep drainage and leaching of salt below the root zone. This paper 6 estimates that 10% of the irrigated land area (producing as much as 40% of the total annual 7 revenue from irrigated land) could be adversely affected by root zone salinity resulting 8 from the adoption of precision irrigation within Australia. The cost of increases in root 9 zone salinisation due to inappropriate irrigation management in the Murray and 10Murrumbidgee Irrigation Areas was estimated at AUD245 m (in 2000/01 dollars) or 13.5% 11 of the revenue from these cropping systems. A review of soil-water and solute movement 12 under precision irrigation systems highlights the gaps in current knowledge including the 13 mismatch between the data required by complex, process-based soil-water or solute 14 simulation models and the data that is easily available from soil survey and routine soil 15

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Modeling Flow Through a One-Dimensional Multi-Layered Soil Profile Using the Method of Lines

Cited by 33 publications

References 18 publications

Ross scheme, Newton–Raphson iterative methods and time-stepping strategies for solving the mixed form of Richards' equation

Ross scheme, Newton–Raphson iterative methods and time-stepping strategies for solving the mixed form of Richards' equation

Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils

Soil–water and solute movement under precision irrigation: knowledge gaps for managing sustainable root zones

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