A control volume scheme using compact integrated radial basis function stencils for solving the Richards equation

Ngo-Cong, Duc; Mai‐Duy, N.; Antille, Diogenes L.; Genuchten, Martinus Th. van

doi:10.1016/j.jhydrol.2019.124240

Cited by 16 publications

(10 citation statements)

References 32 publications

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“…Eqs. (2) and 3were free from the mass conservation problem. The water-based Richards' equation as in Eq.…”

Section: Methodsmentioning

confidence: 99%

“…Richards' equation consists of a governing equation that is used to describe water flow in subsurface porous media such as soil [1]. It is continuously subjected to numerical investigation [2][3][4][5][6][7][8][9].The modeling of water distribution using the equation has important application in climate science, agriculture and also ecosystem management [10]. Among many applications, Zeide [11] has reported the use of Richards' equation in the tree growth modeling prediction.…”

Section: Introductionmentioning

confidence: 99%

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Richards’ Equation: Transition Between Constitutive Equations and the Mechanics of Water Flow in Unsaturated Soil

Giap¹,

Kosuke²

2020

ARAM

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Water flow in soil is normally governed by Richards' partial differential equation. Similarly, the equation can be used to investigate water infiltration in the soil. It is well understood that when water hits the surface of the topsoil, it infiltrates into the soil. However, the mechanics behind the infiltration of water is unknown to many researchers. This study aims to reveal the mechanics behind the well-known Richards' equation that has been used enormously in governing water flow in unsaturated soil since 1931. A classic case study of Haverkamp's water infiltration into Yolo Light Clay was used in the study. The Richards' equation has been discretized using finite difference method and the algebraic solution has been coded into Simply Fortran 2008. The partial differential equation of Richards is supported by two constitutive functions. The functions from Haverkamp and van Genuchten were compared. It is often for researcher to change between the hydraulic functions, which have limitation on the simulation outcome. The solution to overcome the limitation by changing the constitutive function variables was provided.

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“…Eqs. (2) and 3were free from the mass conservation problem. The water-based Richards' equation as in Eq.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Richards’ Equation: Transition Between Constitutive Equations and the Mechanics of Water Flow in Unsaturated Soil

Giap¹,

Kosuke²

2020

ARAM

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“…To do so we consider the new developed code MH-Lump-1D/2D in which the ML technique is implemented for both porous matrix and fractures and a modified version, called MH-Cons-1D/2D, in which ML technique is used only for porous matrix elements and the standard consistent form is used for fractures. To compare these models, we consider the challenging case of infiltration in a dry soil with imposed heads at the top and bottom surfaces (Huang et al 1996;Ngo-Cong et al, 2020). Beside the nonlinearity related to RE, this problem involves an extremely moving sharp front that cannot be captured numerically without introducing dense grids and small time step size.…”

Section: Advantages Of the ML Technique For Fracturesmentioning

confidence: 99%

“…In contrast to the imposed flux boundary condition, the Dirichlet boundary conditions imposed at the soil top surface compound the numerical difficulties as they require an appropriate approach for the evaluation of the equivalent hydraulic conductivity (Belfort et al, 2013). This problem has been widely investigated in the literature and the common question is to develop an accurate solution in such a case (Forsyth and Pruess, 1995;Huang et al, 2002;Arico et al, 2012;Younes et al, 2013;List and Radu, 2016;Islam et al, 2017;Zha et al, 2017;Ngo-Cong et al, 2020). All the exiting studies suggested appropriate numerical solutions for non-fractured domains.…”

Section: Advantages Of the ML Technique For Fracturesmentioning

confidence: 99%

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An advanced discrete fracture model for variably saturated flow in fractured porous media

Koohbor

Fahs

Hoteit

et al. 2020

Advances in Water Resources

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Approximate analytical solution of a soil water movement equation under different ponding radii on the basis of numerical simulation

Luo,

Su,

Tao

et al. 2024

Soil Science Soc of Amer J

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This study addresses the problem of 2D soil water movement under ponding radii of 1, 2, and 3 cm. The soil water movement characteristics (shape parameters of the water content profile, ratio of horizontal wetting front to vertical wetting front, relationship between infiltration time and horizontal wetting front, and relationship between infiltration time and cumulative infiltration) under the above three kinds of water ponding radius were analyzed. On the basis of the assumption that the soil wetting body is a semi‐ellipse and the analytical solution of the 1D soil water movement equation at any angle, the approximate analytical solution of the 2D soil water movement equation under ponding conditions is optimized. The function relationships between infiltration time, wetting front, and cumulative infiltration are established. We applied the numerical data simulated by HYDRUS‐3D to validate the parameters in proposed analytical solutions and evaluated the relationships between the wetting front and hydraulic parameters. The results indicate that as the water ponding radius increases, the wetting body and 2D water content distribution becomes larger. When the water ponding radius was 2 cm, the numerical and analytical solution of 1D soil water distribution showed the best comparison results, and the model error was the smallest. The ratio of wetting fronts was linearly increased with the increase of air‐entry suction with R2 = 0.9969.

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A control volume scheme using compact integrated radial basis function stencils for solving the Richards equation

Abstract: A control volume scheme using compact integrated radial basis function stencils for solving the Richards equation,

Cited by 16 publications

References 32 publications

Richards’ Equation: Transition Between Constitutive Equations and the Mechanics of Water Flow in Unsaturated Soil

Richards’ Equation: Transition Between Constitutive Equations and the Mechanics of Water Flow in Unsaturated Soil

An advanced discrete fracture model for variably saturated flow in fractured porous media

Approximate analytical solution of a soil water movement equation under different ponding radii on the basis of numerical simulation

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