Modeling and numerical simulation of the Richards equation for infiltration problems

Authors

  • Iván Cristian Naula Reina Universidad Central del Ecuador
  • Guillermo Alexis Albuja Proaño Universidad Central del Ecuador
  • René Alfonso Carrillo Flores Universidad Central del Ecuador
  • Carlos Fabián Izurieta Cabrera Universidad Tecnológica Equinoccial

DOI:

https://doi.org/10.29019/enfoqueute.v7n1.87

Keywords:

infiltration, Richards equation, mathematical model, finite elements

Abstract

One of the most important natural resources we have is the soil and it is of great interest to the society to take care of them and not to pollute it. In the study of this issue, we are going to consider one of the most common forms of soil contamination due to an infiltration process. It is therefore that it is essential to address study and clearly understand this process by developing a mathematician model, which will be a representation of this physicist phenomenon. Then design and implement a computer program that simulates the infiltration of liquid pollutants in a given area. In this paper we will develop a mathematical model for two-dimensional infiltration in the saturated zone of porous media, based on the equation in nonlinear partial differential Richards Also, It will present a numerical solution through finite element method and first order This paper shows the computational implementation using a simulator that presents graphically the process of pollution afflicting the ground, exposed to certain pollutants, such as the oil spill in regions of eastern Ecuador, wastewater near industrial complexes, among others, over a certain period of time. Finally, this paper will allow for remedial studies in the case are already contaminated soils or preventive areas established as hazardous.

Downloads

Download data is not yet available.

References

Brezis, H. (1983). Analyse Fonctionnelle. Masson, Paris.
Darcy, H. (1856). Les fontaines publiques de la ville de Dijon. Dalmont, Paris.
Buckingham, E. (1907). Studies on the movement of soil moisture. Washington: USDA
Evans, L.C. (1998). Partial differential Equations. American Mathematical Society. Providence: Graduate Studies in Mathematics.
Blytth, F., Freitas, M (2001). Geología Para Ingenieros. México: Compañía Editorial Continental.
Ehlers,W, Deformation and localization analysis of partially saturated soil, Recuperado 23 de septiembre de 2015. http://www.sciencedirect.com/science/article/pii/S0045782504001148
Gómez, J. Martin, D.. (2010). Análisis Funcional y Optimización. Chile: Universidad de Chile.
Gonzales de Vallejo, L. , I. Ferrer, M. (2002). Ingeniería Geológica. Madrid: Pearson Educacion.
Pino,E., Mejía, J., Abel, E. (Enero, 2012). Modelamiento numérico espacio-temporal 1d de la infiltración basado en la ecuación de Richards y otras simplificadas. Eciperu, 9, 31-36.
Richards, L.. (1931). Capillary conduction of liquids in porous media. USA: Physics, v. 1.
Richards, L.A., Gardner, W.R. Ogata, G. (1956). Physical processes determining water loss from soil. Soil Science Society of American Proceeding 20, 310-314.
Sayas, F. (2007). Modelos Matemáticos en Mecánica. España: Departamento de Matemática Aplicada, Universidad de Zaragoza.

Downloads

Published

2016-03-31

How to Cite

Naula Reina, I. C., Albuja Proaño, G. A., Carrillo Flores, R. A., & Izurieta Cabrera, C. F. (2016). Modeling and numerical simulation of the Richards equation for infiltration problems. Enfoque UTE, 7(1), pp. 46 – 58. https://doi.org/10.29019/enfoqueute.v7n1.87

Issue

Vol. 7 No. 1 (2016)

Section

Miscellaneous

License

The articles and research published by the UTE University are carried out under the Open Access regime in electronic format.  This means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the author. This is in accordance with the BOAI definition of open access. By submitting an article to any of the scientific journals of the UTE University, the author or authors accept these conditions.

The UTE applies the Creative Commons Attribution (CC-BY) license to articles in its scientific journals. Under this open access license, as an author you agree that anyone may reuse your article in whole or in part for any purpose, free of charge, including commercial purposes. Anyone can copy, distribute or reuse the content as long as the author and original source are correctly cited. This facilitates freedom of reuse and also ensures that content can be extracted without barriers for research needs.

 

This work is licensed under a Creative Commons Attribution 3.0 International (CC BY 3.0).

 

The Enfoque UTE journal guarantees and declares that authors always retain all copyrights and full publishing rights without restrictions [© The Author(s)]. Acknowledgment (BY): Any exploitation of the work is allowed, including a commercial purpose, as well as the creation of derivative works, the distribution of which is also allowed without any restriction.