Examples of numerical simulations of two-dimensional unsaturated flow with VS2DI code using different interblock conductivity averaging schemes

Szymkiewicz, Adam; Tisler, Witold; Burzyński, K.

doi:10.1515/logos-2015-0015

Cited by 10 publications

(11 citation statements)

References 18 publications

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“…Following the formulation of Szymkiewicz et al. (2015), based on Richards (1931) and Lappala et al. (1987), in its extended form, it can be expressed as

\begin{matrix} true \\ left \frac{\partial}{\partial x} ([], K_{normals X} K_{r} ((), h) \frac{\partial H}{\partial x}) + \frac{\partial}{\partial z} ([], K_{normals Z} K_{r} ((), h) \frac{\partial H}{\partial z}) + q \\ left = \frac{\partial normalθ}{\partial t} + S_{e} S_{s} \frac{\partial H}{\partial t} \end{matrix}

where

normalθ

is the volumetric water content (dimensionless);

t

is the time [T]; q is a source–sink term [L 3 T −1 ];

S_{normale} = false(θ - {normalθ}_{normalr} false) / false({normalθ}_{normals} - {normalθ}_{normalr} false)

, is the degree of saturation (dimensionless);

θ_{s}

is the saturated water content (dimensionless);

θ_{r}

is the residual water content (dimensionless);

S_{s}

is the specific storage coefficient [L −1 ];

K_{normals X}

and

K_{normals Z}

are the saturated hydraulic conductivity in the X and Z directions [L T −1 ], respectively (vertical coordinate with positive upward direction);

K_{normalr} false(h false)

is the relative hydraulic conductivity (dimensionless) that is a function of h , the water pressure head [L], and H is the total hydraulic head [L] defined as

H = h + z

where z is the po...…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

A methodology for simulating perched conditions in multilayer aquifer systems with 2D variably saturated flow

Aguilera

Heredia

Román

2021

Vadose Zone Journal

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Simulatingflow through multilayer aquifer systems is essential for groundwater management applications such evaluating natural recharge, assessing managed aquifer recharge (MAR), the characterization of surface water–groundwater interactions, and groundwater pollution risk analysis. However, dealing with flow through variably saturated porous media with perched water tables is a difficult task. Usual codes for groundwater flow modeling such as MODFLOW, TOUGH2, and FEFLOW require tedious procedures based on simplified assumptions and approximations. This paper presents a simple approach to simulate two‐dimensional flow through perched aquifers and aquitards in deep vadose zones by combining the Dirichlet and Neumann boundary conditions that may apply to any code simulating unsaturated flow. The proposed approach is illustrated with the unsaturated flow code VS2DTI. The main strengths of the proposed methodology are (a) variably saturated flow in the multilayer system is solved using Richards’ equation, taking into account the lateral flow that sustains observed water levels in perched aquifers and variations in recharge; (b) a Dirichlet‐type boundary condition at the top perched water table is substituted by a Neumann‐type boundary condition, allowing for the representation of any disturbance (e.g., infiltration from ponds, pumping from wells, etc.), regardless of duration and intensity; and (c) the impact of the disturbance is evaluated by comparing the responses of the undisturbed and the disturbed systems. The versatility of this methodology is applied to a MAR case study of a deep aquifer in a sedimentary basin where aquitards limit its feasibility.

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“…Following the formulation of Szymkiewicz et al. (2015), based on Richards (1931) and Lappala et al. (1987), in its extended form, it can be expressed as

\begin{matrix} true \\ left \frac{\partial}{\partial x} ([], K_{normals X} K_{r} ((), h) \frac{\partial H}{\partial x}) + \frac{\partial}{\partial z} ([], K_{normals Z} K_{r} ((), h) \frac{\partial H}{\partial z}) + q \\ left = \frac{\partial normalθ}{\partial t} + S_{e} S_{s} \frac{\partial H}{\partial t} \end{matrix}

where

normalθ

is the volumetric water content (dimensionless);

t

is the time [T]; q is a source–sink term [L 3 T −1 ];

S_{normale} = false(θ - {normalθ}_{normalr} false) / false({normalθ}_{normals} - {normalθ}_{normalr} false)

, is the degree of saturation (dimensionless);

θ_{s}

is the saturated water content (dimensionless);

θ_{r}

is the residual water content (dimensionless);

S_{s}

is the specific storage coefficient [L −1 ];

K_{normals X}

and

K_{normals Z}

are the saturated hydraulic conductivity in the X and Z directions [L T −1 ], respectively (vertical coordinate with positive upward direction);

K_{normalr} false(h false)

is the relative hydraulic conductivity (dimensionless) that is a function of h , the water pressure head [L], and H is the total hydraulic head [L] defined as

H = h + z

where z is the po...…”

Section: Methodsmentioning

confidence: 99%

“…Evaluation of axisymmetric infiltration is one of the most typical applications of VS2DTI (Heilweil et al., 2015; Izbicki, 2002; Szymkiewicz et al., 2015). However, these applications focused either on homogeneous (Heilweil et al., 2015; Szymkiewicz et al., 2015) or heterogeneous (Izbicki, 2002) unconfined aquifers without perched water tables.…”

Section: Methodsmentioning

confidence: 99%

A methodology for simulating perched conditions in multilayer aquifer systems with 2D variably saturated flow

Aguilera

Heredia

Román

2021

Vadose Zone Journal

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“…including coarse sand (Konukcu et al, 2004), sandy soil (Chinkulkijniwat et al, 2016), clayey soil (Szymkiewicz et al, 2015), lateritic soil (Bui Van et al, 2017) and clay (Koerner and Koerner, 2015), were assigned to perform the calculation. Saturated permeability coefficient and van Genuchten parameters these soils are given in Table 1.…”

Section: Simulation Scenarios For Linear Association Analysismentioning

confidence: 99%

Phreatic Surface Estimation In MSE Wall With Geocomposite Back Drainage

Chinkulkijniwat

Horpibulsuk

Duong

et al. 2021

Preprint

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This study proposes a simple mathematic model for approximating the level of phreatic surface inside the protected zone in mechanical stabilized earth wall with back drain installation though the position of phreatic surface at the drainage interface (ho) which reflects the maximum level of phreatic surface in the protected zone. The proposed model was established based on dataset taken from 180 simulation cases caried out in Plaxis environment. Regression results present a combination of significant effects and major role to maximum water level in the protected zone (ho) of a ratio of length from upstream water to the drainage face to the wall height (L/H), a soil permeabilities coefficient (k) and a transmissivity of the drainage material (Tnet). The proposed model can facilitate design of drainage material to achieve desired level of phreatic surface in the protected zone.

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“…Some studies focused on the averaging scheme when heterogeneity is presented (Belfort & Lehmann, ; Belfort, Younes, Fahs, & Lehmann, ; Brunone, Ferrante, Romano, & Santini, ; Romano, Brunoneb, & Santini, ). It is found that different averaging schemes should be used for different flow conditions, and the gravitational and capillary forces have influences on the averaging scheme besides the nodal distance and the soil hydraulic properties (Szymkiewicz, Tisler, & Burzyński, ). Based on the high‐order upwind scheme, An and Noh () developed a high‐order averaging method of hydraulic conductivity for the accurate solution of the RRE.…”

Section: Spatial and Temporal Discretizationmentioning

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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Examples of numerical simulations of two-dimensional unsaturated flow with VS2DI code using different interblock conductivity averaging schemes

Cited by 10 publications

References 18 publications

A methodology for simulating perched conditions in multilayer aquifer systems with 2D variably saturated flow

A methodology for simulating perched conditions in multilayer aquifer systems with 2D variably saturated flow

Phreatic Surface Estimation In MSE Wall With Geocomposite Back Drainage

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

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