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Article

A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam

1
Facultad de Ingeniería Civil, Universidad Michoacana de San Nicolás de Hidalgo, Santiago Tapia 403, Morelia 58000, Mexico
2
Centro de Ciencias Matemáticas, UNAM Campus Morelia, Antigua Carretera a Pátzcuaro 8701, Morelia 58089, Mexico
3
Facultad de Ciencias Físico Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Santiago Tapia 403, Morelia 58000, Mexico
*
Author to whom correspondence should be addressed.
Academic Editor: Theodore E. Simos
Mathematics 2021, 9(14), 1604; https://doi.org/10.3390/math9141604
Received: 20 April 2021 / Revised: 2 July 2021 / Accepted: 3 July 2021 / Published: 7 July 2021
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)
The accurate description of the flow of water in porous media is of the greatest importance due to its numerous applications in several areas (groundwater, soil mechanics, etc.). The nonlinear Richards equation is often used as the governing equation that describes this phenomenon and a large number of research studies aimed to solve it numerically. However, due to the nonlinearity of the constitutive expressions for permeability, it remains a challenging modeling problem. In this paper, the stationary form of Richards’ equation used in saturated soils is solved by two numerical methods: generalized finite differences, an emerging method that has been successfully applied to the transient case, and a finite element method, for benchmarking. The nonlinearity of the solution in both cases is handled using a Newtonian iteration. The comparative results show that a generalized finite difference iteration yields satisfactory results in a standard test problem with a singularity at the boundary. View Full-Text
Keywords: Richards’ equation; generalized finite differences; flow in porous media Richards’ equation; generalized finite differences; flow in porous media
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MDPI and ACS Style

Chávez-Negrete, C.; Santana-Quinteros, D.; Domínguez-Mota, F. A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam. Mathematics 2021, 9, 1604. https://doi.org/10.3390/math9141604

AMA Style

Chávez-Negrete C, Santana-Quinteros D, Domínguez-Mota F. A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam. Mathematics. 2021; 9(14):1604. https://doi.org/10.3390/math9141604

Chicago/Turabian Style

Chávez-Negrete, Carlos, Daniel Santana-Quinteros, and Francisco Domínguez-Mota. 2021. "A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam" Mathematics 9, no. 14: 1604. https://doi.org/10.3390/math9141604

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