Analytical Solution of Richards’ Equation for Application in Automatic Irrigation Systems
International Journal of Theoretical and Applied Mathematics
Volume 3, Issue 5, October 2017, Pages: 163-166
Received: Feb. 20, 2017;
Accepted: Mar. 14, 2017;
Published: Oct. 28, 2017
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Ise Ise Ekpoudom, Department of Electrical, Electronic and Computer Engineering, University of Uyo, Uyo, Nigeria
Anamekere Ime Jacob, Department of Electrical, Electronic and Computer Engineering, University of Uyo, Uyo, Nigeria
Umana Thompson Itaketo, Department of Electrical, Electronic and Computer Engineering, University of Uyo, Uyo, Nigeria
This paper presents the analytical solution to Richards’ equation of hydrology for unsaturated soils. In order to facilitate the design and analysis of a real-time automatic irrigation system, an accurate model must be developed for the system. Richard’s equation of water hydrology may be used to model part of the irrigation system. The major problem with the application of Richard’s equation is in the linearization of the non-linear partial differential equation (PDE). In this paper, an empirical relationship stated by Gardner  was used to linearize the nonlinear PDE. The solution for the PDE was obtained using separation of variables technique.
Ise Ise Ekpoudom,
Anamekere Ime Jacob,
Umana Thompson Itaketo,
Analytical Solution of Richards’ Equation for Application in Automatic Irrigation Systems, International Journal of Theoretical and Applied Mathematics.
Vol. 3, No. 5,
2017, pp. 163-166.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Gardner, W. “Some Steady-State Solutions of the Unsaturated Moisture Low Equation with Application to Evaporation from a Water Table”, Soil Science, Vol. 85, 1958, pp. 228-232.
Kuraz, M., Mayer, P. and Pechm P. “Solving the Non-linear Richards’ Equation Model with Adaptive Domain Decomposition”, Journal of Computational and Applied Mathematics, Vol. 270, 2014, pp 2-11.
Bouchemella, S., Seridi, A. and Alimi-Ichola, I. “Numerical Solution of Water Flow in Unsaturated Soils: Comparative Study of Different Forms of Richards’ Equations” European Journal of Environmental and Civil Engineering, Vol. 9, 2014, pp 1.
Bhosale P. A. and Dixit V. V. ” Water Saving-irrigation Automatic Agricultural Controller”, International Journal of Science and Technology, Volume 1, Number 2, 2012, pp. 34-36.
Israelsen O. W. and Hansen V. E., Irrigation Principle and Practice, John Wiley and Son Inc., 3rd Edition, New Delhi, p 171, 2011.
Hillel, D., Introduction to Environmental Soil Physics, Academic Press, Hardcover, Boston, 2003.
Philip, J. R., “Hydrostatics and Hydrodynamics in Selling Soils”, Water Resources, Res. 5, 1969, pp 1070-1077.
Celia, M. A., Bouloutas, E. T. and Zarba, R. L. “A General Mass-Conservative Numerical Solution for the Unsaturated Flow Equation”, Water Resources Research, Volume 26, Number 7, 1990, pp. 1483-1696.
Majumdar D. K., Irrigation Water Management: Principles and Practice, Eastern Economy Edition, Prentice – Hall of India Private Limited. New Delhi, 2006.
Tracy, F. “Clean Two- And Three-Dimensional Analytical Solutions of Richards' Equation for Testing Numerical Solvers”, Water Resources Research, Vol. 42, Number 8, 2006, pp. 3106-109.
Tracy, F. “Three-Dimensional Analytical Solutions of Richards' Equation for a Box-Shaped Soil Sample with Piecewise-Constant Head Boundary Conditions on the Top”, Journal of Hydrology, Vol. 336, 2007, pp. 391-400.
Warrick, A., Soil Water Dynamics, Oxford University Press, Paperback, New York, 2003.
Genuchten, M. “A Closed-Form Equation for Producing the Hydraulic Conductivity of Unsaturated Soils”, Soil Science American Journal, Vol. 44, 1980, pp. 892-898.