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

Carlos Chávez-Negrete, Daniel Santana-Quinteros and Francisco Domínguez-Mota
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Carlos Chávez-Negrete: Facultad de Ingeniería Civil, Universidad Michoacana de San Nicolás de Hidalgo, Santiago Tapia 403, Morelia 58000, Mexico
Daniel Santana-Quinteros: Centro de Ciencias Matemáticas, UNAM Campus Morelia, Antigua Carretera a Pátzcuaro 8701, Morelia 58089, Mexico
Francisco Domínguez-Mota: Facultad de Ciencias Físico Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Santiago Tapia 403, Morelia 58000, Mexico

Mathematics, 2021, vol. 9, issue 14, 1-14

Abstract: 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.

Keywords: Richards’ equation; generalized finite differences; flow in porous media (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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