Generalized mass-conservative finite volume framework for unified saturated–unsaturated subsurface flow

Dey, Saumava; Dhar, Anirban

doi:10.1016/j.jhydrol.2021.127309

Cited by 6 publications

(3 citation statements)

References 74 publications

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“…Let's consider the three-dimensional Richards-Klute equation, the area Ω of which will be a system of pipes filled with a porous substance (for example, different types of soil). To model the process of mass transfer of a useful substance through such a system of pipes, one can approximate a three-dimensional equation and use numerical methods from works [1][2][3][4][5]. However, to reduce the number of calculations and increase the efficiency of the modeling process, it is advisable to consider some simplification of the system.…”

Section: Problem Formulationmentioning

confidence: 99%

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Richards-Klute Equation on Graphs

Kolesnykov

2023

MCIT

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This paper contains the formulation of the problem of mass transfer in a porous medium on a graph, on the edges of which the one-dimensional problem of mass transfer is modeled using the Richards-Klute equation. To combine separate Richards-Klute equations into a single system, auxiliary mass balance equations are introduced for the vertices of the graph. Problems of approximation of these equations at the vertices of the graph are also discussed.

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Section: Problem Formulationmentioning

confidence: 99%

“…Modifications of standard methods of finite elements [2], finite volumes [3], and finite difference methods [4] are used to increase the efficiency of calculations. Also, papers [5] propose linearization of the Richards-Klute equation.…”

Section: Introductionmentioning

confidence: 99%

Richards-Klute Equation on Graphs

Kolesnykov

2023

MCIT

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“…Because of the limitations of the existing multidimensional modeling for the transport of PFAS in unsaturated porous media with the transient water flow and the variable surface tension, we propose a multidimensional modeling approach based on the second-order accurate implicit finite volume method (FVM). The FVM has been employed for solving the transient water flow in unsaturated porous media (Dey & Dhar, 2022;Lai & Ogden, 2015). The features of our modeling approach are as follows.…”

Section: Introductionmentioning

confidence: 99%

Second-order accurate implicit finite volume method for multidimensional modeling of PFAS transport in unsaturated porous media with variable surface tension

Sun

Szymczak

et al. 2022

Preprint

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Per- and polyfluoroalkyl substances (PFASs) have become emerging contaminants of critical concern. Comprehensive understanding of the transport and fate of PFAS in the vadose-zone, a type of water-unsaturated porous media, is key to determination of the risks of the PFAS contamination in the subsurface and to the development of the effective remediation strategies. Accurate modeling of the PFAS transport in the unsaturated porous media is still a challenge due to the variable surface tension induced by the adsorption of PFAS to the air-water interfaces. In an effort to address this challenge, we propose a multidimensional modeling framework for the transient PFAS transport in the unsaturated porous media based on the second order accuracy finite volume method. In the modeling, the adsorption of PFAS to the solid surfaces and to the air-water interfaces is described by the two-domain sorption kinetics model, i.e., both the instantaneous and the rate limited PFAS adsorptions are taken into account. The diffusive and convective terms in the governing equations for the PFAS transport and the water flow are discretized by the central difference and the quadratic upstream interpolation for convective kinetics schemes, respectively. Both of these two schemes have the second order accuracy. We investigate the effects of the convergent criteria, coupling method, and variation of the surface tension on the average and the local PFAS concentration and water content in the computational domain. We find that the convergent criteria should be chosen carefully so as to get the accurate results. The differences between the different coupling methods are affected by the boundary conditions. The variation in the surface tension due to the variation of the PFAS concentration cannot be neglected. These studies not only guide the numerical schemes used in the modeling but also provide the insights into the transport of PFAS in unsaturated porous media. The multidimensional modeling framework presented in this work can be further extended to explore in detail the transport of PFAS in the vadose-zone.

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A reduced-order framework for three-dimensional-equivalent confined groundwater modeling with emphasis on well-boundary implementation

Dey,

Dhar

2023

Hydrogeol J

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Generalized mass-conservative finite volume framework for unified saturated–unsaturated subsurface flow

Cited by 6 publications

References 74 publications

Richards-Klute Equation on Graphs

Richards-Klute Equation on Graphs

Second-order accurate implicit finite volume method for multidimensional modeling of PFAS transport in unsaturated porous media with variable surface tension

A reduced-order framework for three-dimensional-equivalent confined groundwater modeling with emphasis on well-boundary implementation

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