A mass-conservative switching algorithm for modeling fluid flow in variably saturated porous media

Zadeh, Kouroush Sadegh

doi:10.1016/j.jcp.2010.10.011

Cited by 35 publications

(8 citation statements)

References 58 publications

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“…An experiment consisting of free drainage in a 600 cm deep lysimeter filled with a material with silty sand texture conducted at the Los Alamos National Laboratory ( Abeele, 1984 ) is often used to validate one-dimensional schemes for unsaturated flows (see e.g., ( Zadeh, 2011;Zambra et al, 2012;Caviedes-Voullième et al, 2013 )). This example is provided with the hydrus 1d software ( Simunek et al, 2008 ), which is also used for validation purposes in the papers cited above.…”

Section: Comparison With Experiments and Exact Solutions For Unsatura...mentioning

confidence: 99%

“…12) . An improved prediction of the pressure profiles is obtained in Zadeh (2011) with slightly modified parameters of the van Genuchten-Mualem model, but with the price of larger deviations for the water content.…”

Section: Comparison With Experiments and Exact Solutions For Unsatura...mentioning

confidence: 99%

“…4) . infiltration into dry media ( Zadeh, 2011 ), and is well suited to analytical approaches ( Philip, 1969;Warrick et al, 1985;Sander et al, 1988 ). Philip ( Philip, 1969 ) derived an exact solution for infiltration problems expressed in the form 𝑧 ( 𝜃, 𝑡 ) , that is, the depth where the water content takes specified values at given time points 𝑡 .…”

Section: Figmentioning

confidence: 99%

“…The GRW scheme for one-dimensional solutions of the Richards equation, which captures the transition from unsaturated to saturated flow regimes is validated by comparisons with solutions provided by richy software, based on the mixed finite element method (MFEM), with backward Euler discretization in time and Newton linearization, developed at the Mathematics Department of the Friedrich-Alexander University of Erlangen-Nürnberg ( Schneid et al, 2000;Schneid, 2000 ). For the particular case of unsaturated flows, the one-dimensional GRW solutions are also tested by comparisons with experimental data ( Zadeh, 2011;Zambra et al, 2012 ) and exact solutions published in the literature ( Warrick et al, 1985;Watson et al, 1995 ). The two-dimensional GRW solutions are compared on benchmark problems with two-point flux approximation (TPFA) finite volume solvers using backward Euler discretization in time and 𝐿 -scheme linearization .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media

Suciu¹,

Illiano²,

Prechtel³

et al. 2021

Preprint

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We present new random walk methods to solve flow and transport problems in saturated/unsaturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic conductivity and recharge fields, processes at the field and regional scales. The numerical schemes are based on global random walk algorithms (GRW) which approximate the solution by moving large numbers of computational particles on regular lattices according to specific random walk rules. To cope with the nonlinearity and the degeneracy of the Richards equation and of the coupled system, we implemented the GRW algorithms by employing linearization techniques similar to the L-scheme developed in finite element/volume approaches. The resulting GRW L-schemes converge with the number of iterations and provide numerical solutions that are first-order accurate in time and second-order in space. A remarkable property of the flow and transport GRW solutions is that they are practically free of numerical diffusion. The GRW solvers are validated by comparisons with mixed finite element and finite volume solvers in one- and two-dimensional benchmark problems. They include Richards' equation fully coupled with the advection-diffusion-reaction equation and capture the transition from unsaturated to saturated flow regimes. &#160;For completeness, we also consider decoupled flow and transport model problems for saturated aquifers.

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Section: Comparison With Experiments and Exact Solutions For Unsatura...mentioning

confidence: 99%

Section: Comparison With Experiments and Exact Solutions For Unsatura...mentioning

confidence: 99%

Section: Figmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media

Suciu¹,

Illiano²,

Prechtel³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Starting from Celia et al (), further studies have been carried out to improve the mass conservation while maintaining a manageable computational cost. Hao, Zhang, and Kravchenko () proposed to apply Celia's algorithm only if the change of pressure head between time steps is larger than the threshold value (e.g., 3–5 cm), while Sadegh Zadeh () suggested using Celia's algorithm when the nodal head value is less than the threshold value (e.g., −2.5 cm). However, it was demonstrated that Celia's algorithm was sufficiently robust and efficient in terms of mass conservation, and thus these hybrid methods were criticized to be unnecessary (He, Shao, Kolditz, Wang, & Kalbacher, ).…”

Section: Different Forms Of Rresmentioning

confidence: 99%

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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Toward a new parameterization of hydraulic conductivity in climate models: Simulation of rapid groundwater fluctuations in Northern California

Vrettas

Fung

2015

J Adv Model Earth Syst

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Preferential flow through weathered bedrock leads to rapid rise of the water table after the first rainstorms and significant water storage (also known as ''rock moisture'') in the fractures. We present a new parameterization of hydraulic conductivity that captures the preferential flow and is easy to implement in global climate models. To mimic the naturally varying heterogeneity with depth in the subsurface, the model represents the hydraulic conductivity as a product of the effective saturation and a background hydraulic conductivity K bkg , drawn from a lognormal distribution. The mean of the background K bkg decreases monotonically with depth, while its variance reduces with the effective saturation. Model parameters are derived by assimilating into Richards' equation 6 years of 30 min observations of precipitation (mm) and water table depths (m), from seven wells along a steep hillslope in the Eel River watershed in Northern California. The results show that the observed rapid penetration of precipitation and the fast rise of the water table from the well locations, after the first winter rains, are well captured with the new stochastic approach in contrast to the standard van Genuchten model of hydraulic conductivity, which requires significantly higher levels of saturated soils to produce the same results. ''Rock moisture,'' the moisture between the soil mantle and the water table, comprises 30% of the moisture because of the great depth of the weathered bedrock layer and could be a potential source of moisture to sustain trees through extended dry periods. Furthermore, storage of moisture in the soil mantle is smaller, implying less surface runoff and less evaporation, with the proposed new model.

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A mass-conservative switching algorithm for modeling fluid flow in variably saturated porous media

Cited by 35 publications

References 58 publications

Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media

Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media

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

Toward a new parameterization of hydraulic conductivity in climate models: Simulation of rapid groundwater fluctuations in Northern California

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